Loans (1)

Chhavi Verma
Chhavi VermaStudent of poornima college of engineering
TYPES OF LOANS
• PURE DISCOUNT
• INTEREST ONLY
• CONSTANT PAYMENT
TYPES OF LOANS
PURE DISCOUNT LOANS
PURE DISCOUNT LOANS: the borrower receives the money
today and repays the loan in one lump sum at some time
in the future.
Example: you borrow $10,000 today and agree to repay the
loan with 9% annual interest (compounded annually) five
years from today. What is your loan balance in five years?
FV = $10,000 (1 + 0.09)5 = $15,386.24
TYPES OF LOANS
PURE DISCOUNT LOANS
Another example:
Treasury Bills -- for historical reasons,
the interest rate on a T-Bill is quoted as a discount:
interest rate quoted = interest paid/par value.
For example, the quoted rate on a one year $10,000 T-Bill at
7% interest is:
Par value
$10,000.00
Present value
$ 9,345.79
Interest paid
$ 654.21
The interest rate quoted is $654.21/$10,000 = 6.54%
(even though the interest rate is 7%).
TYPES OF LOANS
INTEREST ONLY LOANS
INTEREST ONLY LOAN: the borrower receives the money
today and agrees to pay the lender interest periodically over
the loan term and the principal (the original loan amount) at
the end of the loan term.
Example: you borrow $10,000 today and agree to pay interest
annually at the annual rate of 9% and repay the principal at
the end of five years. What is your annual interest payment?
Interest

= 0.09 x $10,000

= $900
TYPES OF LOANS
CONSTANT PAYMENT LOANS

•
•
•
•

FIXED RATE OF INTEREST
FIXED LOAN TERM
FULLY AMORTIZING
FIXED PERIODIC PAYMENTS
TYPES OF LOANS
CONSTANT PAYMENT LOANS
Computing the equal periodic payment for amortized loans:
PMT = Loan Amount

where
CR
n
k
PMT

=
=
=
=

1
nk

1
∑1 CR t
t = (1 +
)
k

the annual contract rate of interest
the number of years in the loan term
the number of payments per year
the equal periodic payment necessary to fully
amortize the Loan Amount with nk payments.
TYPES OF LOANS
CONSTANT PAYMENT LOANS
Compute the monthly payment necessary to fully amortize a
30 year, 8% annual interest (compounded monthly), $100,000
loan.
PMT =

$100,000
=
360
1
∑ 0.08 t
t = (1 +
1
)
12

Annual debt service (DS)

$ 733.76

= 12 x PMT = $8,805.12
TYPES OF LOANS
CONSTANT PAYMENT LOANS
For a fixed rate, fixed term, fixed payment, fully amortizing
loan, the mortgage balance (book value of the loan) is simply
the present value of the remaining stream of payments
discounted at the periodic contract rate.
Let

MBs

= mortgage balance at the end of period s
= PMT

nk −s

1
∑ CR t
t = (1 +
1
)
k
TYPES OF LOANS
CONSTANT PAYMENT LOANS
What is the mortgage balance in five years for a $100,000, 30
year, 8% annual interest rate, monthly payment loan?
The mortgage balance in five years is the present value of the
300 (360-60) remaining monthly payments discounted at the
monthly rate of 0.08/12.
300

MB60

1
= $733.76 ∑
= $ 95,069.26
0.08 t
t = (1 +
1
)
12
TYPES OF LOANS
CONSTANT PAYMENT LOANS
Alternatively, the mortgage balance is the future value (FV)
in:
s

1
MBs
PV = PMT ∑
+
CR t
CR s
t =1 (1 +
) (1 +
)
k
k
60

1
MBs
$100,000 = $733.76∑
+
0.08 t
0.08 60
t =1 (1 +
) (1 +
)
12
12
TYPES OF LOANS
CONSTANT PAYMENT LOANS
Amortization schedules separate the periodic payment into
interest and principal:
Periodic interest payment = beginning balance x periodic rate
or Is = MBs-1
Periodic principal

CR
k
= periodic payment - periodic interest

or Ps = PMT - Is
TYPES OF LOANS
CONSTANT PAYMENT LOANS
Separate the $733.76 monthly payment into interest and
principal for the first two months of the $100,000, 30 year, 8%
annual interest rate loan.
Month 1:
Interest
= $100,000.00 x 0.0066667 = $666.67
Principal = $733.76 - $666.67
= $ 67.09
MB1
= $100,000.00 - $67.09 = $99,932.91
Month 2:
Interest
= $99,932.91 x 0.0066667 = $666.22
Principal = $733.76 - $666.22
= $ 67.54
MB2
= $99,932.91 - $ 67.54
= $99,865.37
TYPES OF LOANS
CONSTANT PAYMENT LOANS
How would you calculate the amount of interest you paid
during the fifth year of a conventional mortgage?
You could separate the monthly payments into interest and
principal for the 12 months of the fifth year and add the
monthly interest payments.
Fortunately, there’s an easier way:
Principal paid between months s and t = MBs - MBt
Interest paid = PMT (t - s) - Principal paid
TYPES OF LOANS
CONSTANT PAYMENT LOANS
Compute the principal and interest paid during the fifth year of
a $100,000, 30 year, 8% annual rate, monthly payment
mortgage.
312

MB48

1
= $733.76 ∑
0.08 t
t = (1 +
1
)
12

= $96,218.44

300

MB60 = $733.76

1
∑ 0.08 t
t = (1 +
1
)
12

= $95,069.26

Year 5:
Principal paid: $96,218.44 - $95,069.26 = $1,149.17
Interest paid: $733.76 x 12 - $1,149.17 = $7,655.95
TYPES OF LOANS
CONSTANT PAYMENT LOANS
In what month is one half of the loan repaid?

s

1
$50,000
$100,000 = $733.76∑
+
0.08 t
.08 s
t = 1 (1 +
) (1 +
)
12
12
s = 269 (the 5th month of year 22)
Constant Payment Mortgages:
Yields
The lender’s expected yield or borrower’s true borrowing
cost is the IRR on the expected mortgage cash flows.
Let

Fee
= loan origination fee,
Points = discount points in dollars (points are usually
expressed as a percent of the loan amount),
S
= month that the loan is repaid,
PP
= the dollar amount of the prepayment
penalty (a percent of the mortgage balance),
NLA = net loan amount
= Loan Amount - Fee - Points
y
= the discount rate -- the lender’s yield, the
borrower’s borrowing cost.
Constant Payment Mortgages:
Yields
Computing Lender’s Yield (or Borrower’s Borrowing Cost)
There are 3 cases to consider:
(1)

The loan is held to maturity;

(2)

the loan is repaid prior to maturity without
penalty;

(3)

the loan is repaid prior to maturity with a
prepayment penalty.
Constant Payment Mortgages:
Yields
Computing Lender’s Yield (or Borrower’s Borrowing Cost)

1)

If the loan is held to maturity, solve for y in:

nk

1
NLA = PMT ∑
t
t =1 (1 + y / 12 )
Constant Payment Mortgages:
Yields
Example: compute the lender’s expected yield (or the
borrower’s borrowing cost) for a $100,000, 30 year,
monthly payment mortgage that has a 7.5% annual contract
rate of interest if the lender charges a $1,000 loan
origination fee, 2 discount points, and expects the borrower
to hold the loan to maturity.
NLA = $100,000 - $1,000 - $2,000
PMT =

360

= $97,000.00

1
=
$100,000 / ∑
0.075 t
t = (1 +
1
)
12

$699.21
Constant Payment Mortgages:
Yields
Example (continued): the lender’s expected yield (or the
borrower’s true borrowing cost) is the IRR (or discount rate y)
in the following:
360

1

t =1

y t
(1 + )
12

$97,000 = $699.21∑

y = 7.81%
Constant Payment Mortgages:
Yields
Computing Lender’s Yield (or Borrower’s Borrowing Cost)
(2)

If the loan is repaid prior to maturity without penalty,
solve for y in:
s

1

MBS
NLA = PMT ∑
+
y t
y s
t =1 (1 +
) (1 + )
12
12
Constant Payment Mortgages:
Yields
Example: compute the lender’s expected yield (or borrower’s
borrowing cost) in the previous example if the lender expects
the borrower to repay the loan, without penalty, at the end of
four years.
312

1
MB48 = $699.21∑
= $95,860.00
0.075 t
t =1 (1 +
)
12
Solve for y = 8.40% in:
48

1

$95,860.00
$97,000 = $699.21∑
+
y t
y 48
t =1 (1 +
)
(1 + )
12
12
Constant Payment Mortgages:
Yields
Computing Lender’s Yield (or Borrower’s Borrowing Cost)
(3)

If the loan is repaid prior to maturity with a prepayment
penalty, solve for y in:

MBS + PPS
NLA = PMT ∑
+
y t
y s
t = 1 (1 +
)
(1 + )
12
12
s

1

Prepayment penalties are computed as a percent of the
outstanding mortgage balance.
Constant Payment Mortgages:
Yields
Example: compute the lender’s expected yield (or borrower’s
borrowing cost) in the previous example if the lender expects
the borrower to repay the loan, with a 2% prepayment penalty,
at the end of four years.

$95,860.00 + $1,917.20
$97,000 = $699.21∑
+
y t
y 48
t = 1 (1 +
)
(1 + )
12
12
48

1

FV = $97,777.20 and y = 8.82%
Constant Payment Mortgages:
Yields
Relationship between mortgage yields and prepayment (with no
prepayment penalty) for a 7.5%, 30 year, constant payment
mortgage with a $1,000 loan fee and 2 discount points.
Year of Prepayment
1
2
3
4
5
10
20
30

Mortgage Yield
10.69%
9.16%
8.65%
8.40%
8.25%
7.96%
7.83%
7.81%
Constant Payment Mortgages:
Yields

The Annual Percentage Rate (APR) on a loan is the lender’s
yield (or borrower’s borrowing cost) computed assuming the
loan is held to maturity rounded to the nearest one-eighth.

The APR for the loan in the previous example is

7

3
.
4
Constant Payment Mortgages:
Yields
Charging Points to Achieve a Desired Yield
If a lender has a required yield of y, then the points the lender
must charge to obtain the required yield are computed by
solving for ‘Points’ in:

MB s + PPs
1
Loan Amount − Points − Fee = PMT∑
+
y
y
t =1
(1 + ) t
(1 + ) s
12
12
s
Constant Payment Mortgages:
Yields
Example: compute the points a lender must charge to earn a
9% required yield on a $100,000, 30 year, 7.5% annual
interest rate, monthly payment mortgage if the lender
charges a $1,000 loan origination fee and expects the
borrower to repay the loan, without penalty, at the end of
four years.
48

1
$95,860.00
$100,000 − Points − $1,000 = $699.21∑
+
0.09 t
0.09 48
t= 1
(1 +
) (1 +
)
12
12

$99,000 - Points = $95,066.75;

Points = $3,933.25
Alternative Mortgage Instruments
• Graduated Payment Mortgages (GPMs)
• Price Level Adjusted Mortgages (PLAMs)
• Adjustable Rate Mortgages (ARMs)
• Reverse Annuity Mortgages (RAMs)
• Shared Appreciation Mortgages (SAMs)
Alternative Mortgage Instruments
Graduated Payment Mortgage
Fixed
• Contract Rate
Fixed
• Loan Term
Payments Increase During First Few Years
•
Payments Known in Advance
•
Permit
• Negative Amortization
Alternative Mortgage Instruments
Graduated Payment Mortgage
Loan
Rate
Term

=
=
=

$100,000
12%
30 years with monthly payments;
payment increases 7.5% per year for first five years

Year
1
2
3
4
5
6-30

Monthly
Payment
$ 791.38
850.73
914.54
983.13
1,056.86
1,136.13

Monthly
Interest
$ 1,000.00
1,026.46
1,048.75
1,065.77
1,076.25

Ending
Balance
$ 102,645.82
104,874.52
106,576.64
107,624.72
107,870.63
Alternative Mortgage Instruments
Price Level Adjusted Mortgage
For a fixed payment mortgage, the contract rate of interest, CR, is:
CR = rf + ρ
+ inf
where rf = risk free rate
=
ρ risk premium
inf = expected inflation rate
With a Price Level Adjusted Mortgage (PLAM),
CR = rf + ρ
and the outstanding mortgage balance is indexed to the price level
to compensate the lender for inflation.
Alternative Mortgage Instruments
Price Level Adjusted Mortgage
Loan
Rate
Term
Inf

=
=
=
=

Year
1
2
3

$100,000
5%
30 years with monthly payments
5%, 6%, and 4%
Beginning
Balance
$ 100,000.00
103,450.55
107,931.31

Monthly
Payment
$ 536.82
563.66
597.48

Ending Balance
Before
After
$ 98,524.34 $ 103,450.55
101,821.99
107,931.31
106,116.98
110,361.66
Alternative Mortgage Instruments
Adjustable Rate Mortgages
Contract
• Rate Indexed to Lender’s Cost of Funds (plus a margin)
Term
•May Adjust
Monthly
• Payment May Adjust
Negative
• Amortization May be Permitted
Typically Have Periodic and Lifetime Interest Rate Caps
•
Alternative Mortgage Instruments
Adjustable Rate Mortgages
Loan
Initial Rate
Term
Index
Margin
Caps
Year
1
2
3

=
=
=
=
=
=

$100,000
9%
30 years with monthly payments
Yields on 1-Year Treasury Securities ( 8%, 9%, 7%)
2.5%
2/5—200bp annual cap and 500bp lifetime cap

Beginning
Balance
$ 100,000.00
99,316.84
98,815.85

Interest Rates
Market
Contract
9.0%
9.0%
11.5%
11.0%
9.5%
9.5%

Monthly
Payment
$ 804.62
950.09
841.79
Alternative Mortgage Instruments
Reverse Annuity Mortgages
The borrower:
receives the loan in periodic installments
•
repays the loan in one lump sum at the end of the term
•
The monthly RAM receipt on a 10 year, $50,000, 8% annual interest rate
RAM is $273.30. The borrower will recieve 120 of these monthly
payments. At the end of the loan term, the borrower will repay the lender
$50,000.
Principal = 120 x $ 273.30

=

$ 32,796.56

Interest = $50,000 - 32,796.56

=

$ 17,203.44
Alternative Mortgage Instruments
Shared Appreciation Mortgages
The lender provides the borrower with:
a below
• market rate of interest, or
cash
•to pay a portion of the down payment,
or both
•
In exchange for a share of the property value appreciation during the
hoding period.
1 de 37

Recomendados

Bab 6 - Accounting and the Time Value of Money por
Bab 6 - Accounting and the Time Value of MoneyBab 6 - Accounting and the Time Value of Money
Bab 6 - Accounting and the Time Value of Moneymsahuleka
6.9K visualizações59 slides
diskon tunai dan tingkat diskonto por
diskon tunai dan tingkat diskontodiskon tunai dan tingkat diskonto
diskon tunai dan tingkat diskontoUniversity of Muhammadiyah Sukabumi
709 visualizações15 slides
Chapter 6 Lecture por
Chapter 6 LectureChapter 6 Lecture
Chapter 6 LectureSharonLong
2.7K visualizações42 slides
Time Value of Money por
Time Value of MoneyTime Value of Money
Time Value of MoneyJi Li
3.6K visualizações56 slides
Chap010 por
Chap010Chap010
Chap010mselaoudiy
934 visualizações40 slides
How does the math work por
How does the math workHow does the math work
How does the math workBrooke Clark
30 visualizações25 slides

Mais conteúdo relacionado

Mais procurados

Chapter 6 microeconomics por
Chapter 6 microeconomicsChapter 6 microeconomics
Chapter 6 microeconomicsNoor Asma Zakaria
2.5K visualizações54 slides
Present value por
Present valuePresent value
Present valueCA Yash Jagati
9.2K visualizações37 slides
GSB711-Lecture-Note-03-The-Time-Value-of-Money por
GSB711-Lecture-Note-03-The-Time-Value-of-MoneyGSB711-Lecture-Note-03-The-Time-Value-of-Money
GSB711-Lecture-Note-03-The-Time-Value-of-MoneyUniversity of New England
8.3K visualizações40 slides
Calculating Mortgage Loans por
Calculating Mortgage LoansCalculating Mortgage Loans
Calculating Mortgage Loanswindiee Green
250 visualizações3 slides
Time value of money por
Time value of moneyTime value of money
Time value of moneyAnkit Jain
17.5K visualizações48 slides
Bond price and yield pdf por
Bond price and yield pdfBond price and yield pdf
Bond price and yield pdfDavid Keck
3.3K visualizações39 slides

Mais procurados(20)

Chapter 6 microeconomics por Noor Asma Zakaria
Chapter 6 microeconomicsChapter 6 microeconomics
Chapter 6 microeconomics
Noor Asma Zakaria2.5K visualizações
Present value por CA Yash Jagati
Present valuePresent value
Present value
CA Yash Jagati9.2K visualizações
GSB711-Lecture-Note-03-The-Time-Value-of-Money por University of New England
GSB711-Lecture-Note-03-The-Time-Value-of-MoneyGSB711-Lecture-Note-03-The-Time-Value-of-Money
GSB711-Lecture-Note-03-The-Time-Value-of-Money
University of New England8.3K visualizações
Calculating Mortgage Loans por windiee Green
Calculating Mortgage LoansCalculating Mortgage Loans
Calculating Mortgage Loans
windiee Green250 visualizações
Time value of money por Ankit Jain
Time value of moneyTime value of money
Time value of money
Ankit Jain17.5K visualizações
Bond price and yield pdf por David Keck
Bond price and yield pdfBond price and yield pdf
Bond price and yield pdf
David Keck3.3K visualizações
Time Value of Money (Financial Management) por Qasim Raza
Time Value of Money (Financial Management)Time Value of Money (Financial Management)
Time Value of Money (Financial Management)
Qasim Raza12.5K visualizações
Liabilitas jangka panjang por iyandri tiluk wahyono
Liabilitas jangka panjangLiabilitas jangka panjang
Liabilitas jangka panjang
iyandri tiluk wahyono15.4K visualizações
Ape 3.presentacion y solucion de ejercicios 1 por alexandraalejandro5
Ape 3.presentacion y solucion de ejercicios 1Ape 3.presentacion y solucion de ejercicios 1
Ape 3.presentacion y solucion de ejercicios 1
alexandraalejandro583 visualizações
Ch13 por helal682621
Ch13Ch13
Ch13
helal6826215.5K visualizações
The valuation of long-term securities por Zubair Arshad
The valuation of long-term securitiesThe valuation of long-term securities
The valuation of long-term securities
Zubair Arshad12.6K visualizações
Time value of money por Mahesh Kadam
Time value of moneyTime value of money
Time value of money
Mahesh Kadam267 visualizações
Time Value of Money por Fahim Muntaha
Time Value of MoneyTime Value of Money
Time Value of Money
Fahim Muntaha8.2K visualizações
time value of money por ashfaque75
time value of moneytime value of money
time value of money
ashfaque75655 visualizações
The Time Value of Money por milfamln
The Time Value of MoneyThe Time Value of Money
The Time Value of Money
milfamln6K visualizações
Time volue of money por Zubair Arshad
Time volue of moneyTime volue of money
Time volue of money
Zubair Arshad2.1K visualizações
Financial Management assignment Questions Answers por Total Assignment Help
Financial Management assignment Questions AnswersFinancial Management assignment Questions Answers
Financial Management assignment Questions Answers
Total Assignment Help54 visualizações
Interest Rates and Bond Evaluation by Junaid Chohan por Junaid Ashraf
Interest Rates and Bond Evaluation by Junaid ChohanInterest Rates and Bond Evaluation by Junaid Chohan
Interest Rates and Bond Evaluation by Junaid Chohan
Junaid Ashraf5.5K visualizações
Bond valuation por privatebankerro
Bond valuationBond valuation
Bond valuation
privatebankerro8.3K visualizações

Destaque

business failures in Jaffna por
business failures in Jaffnabusiness failures in Jaffna
business failures in JaffnaUniversity of Jaffna
1.4K visualizações15 slides
Top Reasons Small Businesses Fail por
Top Reasons Small Businesses Fail Top Reasons Small Businesses Fail
Top Reasons Small Businesses Fail BizcentralUSA
1.2K visualizações17 slides
Banking in the early 20th century por
Banking in the early 20th centuryBanking in the early 20th century
Banking in the early 20th centuryEmily Holmes
2.1K visualizações6 slides
Why do businesses fail por
Why do businesses failWhy do businesses fail
Why do businesses failAndy Goodwin
1.5K visualizações6 slides
PwC Portfolio Advisory Group Market Survey - March 2015 por
PwC Portfolio Advisory Group Market Survey - March 2015PwC Portfolio Advisory Group Market Survey - March 2015
PwC Portfolio Advisory Group Market Survey - March 2015Thorsten Lederer 托尔斯滕
2K visualizações16 slides
Credit default of banks in Bangladesh por
Credit default of banks in BangladeshCredit default of banks in Bangladesh
Credit default of banks in BangladeshMd. Abu Naser
881 visualizações5 slides

Destaque(16)

business failures in Jaffna por University of Jaffna
business failures in Jaffnabusiness failures in Jaffna
business failures in Jaffna
University of Jaffna1.4K visualizações
Top Reasons Small Businesses Fail por BizcentralUSA
Top Reasons Small Businesses Fail Top Reasons Small Businesses Fail
Top Reasons Small Businesses Fail
BizcentralUSA1.2K visualizações
Banking in the early 20th century por Emily Holmes
Banking in the early 20th centuryBanking in the early 20th century
Banking in the early 20th century
Emily Holmes2.1K visualizações
Why do businesses fail por Andy Goodwin
Why do businesses failWhy do businesses fail
Why do businesses fail
Andy Goodwin1.5K visualizações
Credit default of banks in Bangladesh por Md. Abu Naser
Credit default of banks in BangladeshCredit default of banks in Bangladesh
Credit default of banks in Bangladesh
Md. Abu Naser881 visualizações
Loans and discount function (Book: Money, Credit and Banking by Cristobal M P... por theMAUIreturns
Loans and discount function (Book: Money, Credit and Banking by Cristobal M P...Loans and discount function (Book: Money, Credit and Banking by Cristobal M P...
Loans and discount function (Book: Money, Credit and Banking by Cristobal M P...
theMAUIreturns6.1K visualizações
10 Common Reasons For Small Business Failure por Experian
10 Common Reasons For Small Business Failure10 Common Reasons For Small Business Failure
10 Common Reasons For Small Business Failure
Experian7.2K visualizações
Non Performing Loans (NPL‘s) – how to handle and optimize por László Árvai
Non Performing Loans (NPL‘s) – how to handle and optimizeNon Performing Loans (NPL‘s) – how to handle and optimize
Non Performing Loans (NPL‘s) – how to handle and optimize
László Árvai5.9K visualizações
Top 5 Reasons Businesses Fail Presentation por Tom Hackelman
Top 5 Reasons Businesses Fail PresentationTop 5 Reasons Businesses Fail Presentation
Top 5 Reasons Businesses Fail Presentation
Tom Hackelman11.5K visualizações
13 credit & loan functions por maynardteacher
13 credit & loan functions13 credit & loan functions
13 credit & loan functions
maynardteacher2.5K visualizações
The Impact of Liquidity on Profitability on Selected Banks of Bangladesh por Samia Ibrahim
The Impact of Liquidity on Profitability on Selected Banks of Bangladesh The Impact of Liquidity on Profitability on Selected Banks of Bangladesh
The Impact of Liquidity on Profitability on Selected Banks of Bangladesh
Samia Ibrahim7.1K visualizações
Functions of banks por Neeta Sharma
Functions of banksFunctions of banks
Functions of banks
Neeta Sharma181.7K visualizações
6 Reasons Your Small Business Will Fail (and How to Avoid Them) por Palo Alto Software
6 Reasons Your Small Business Will Fail (and How to Avoid Them)6 Reasons Your Small Business Will Fail (and How to Avoid Them)
6 Reasons Your Small Business Will Fail (and How to Avoid Them)
Palo Alto Software150.8K visualizações
Feasibility report -basic concepts with example por Abhijeet Bhosale
Feasibility report -basic concepts with exampleFeasibility report -basic concepts with example
Feasibility report -basic concepts with example
Abhijeet Bhosale586.8K visualizações
Project planning and feasibility study por Mars Mfyam
Project planning and feasibility studyProject planning and feasibility study
Project planning and feasibility study
Mars Mfyam312.2K visualizações

Similar a Loans (1)

chapter_10.ppt por
chapter_10.pptchapter_10.ppt
chapter_10.pptDr. Ahmed Hassan, PhD, DBA, PMP
9 visualizações60 slides
Comparing Rates por
Comparing RatesComparing Rates
Comparing RatesCarrine Aulia
2K visualizações26 slides
Chap006 por
Chap006Chap006
Chap006Morten Andersen
1.1K visualizações25 slides
Actuarial Statistics por
Actuarial StatisticsActuarial Statistics
Actuarial StatisticsMary Montoya
4 visualizações48 slides
Bond valuation por
Bond valuationBond valuation
Bond valuationBabasab Patil
6.5K visualizações59 slides
Time Value of Money- Apendix-G por
Time Value of Money- Apendix-GTime Value of Money- Apendix-G
Time Value of Money- Apendix-GSovann Nuon
1.4K visualizações28 slides

Similar a Loans (1)(20)

Comparing Rates por Carrine Aulia
Comparing RatesComparing Rates
Comparing Rates
Carrine Aulia2K visualizações
Chap006 por Morten Andersen
Chap006Chap006
Chap006
Morten Andersen1.1K visualizações
Actuarial Statistics por Mary Montoya
Actuarial StatisticsActuarial Statistics
Actuarial Statistics
Mary Montoya4 visualizações
Bond valuation por Babasab Patil
Bond valuationBond valuation
Bond valuation
Babasab Patil6.5K visualizações
Time Value of Money- Apendix-G por Sovann Nuon
Time Value of Money- Apendix-GTime Value of Money- Apendix-G
Time Value of Money- Apendix-G
Sovann Nuon1.4K visualizações
Ross7e ch04 por Alfredo Vasquez
Ross7e ch04Ross7e ch04
Ross7e ch04
Alfredo Vasquez731 visualizações
Aminullah assagaf financial management p1621_ch. 16 sd 21_28 mei 2021 por Aminullah Assagaf
Aminullah assagaf financial management p1621_ch. 16 sd 21_28 mei 2021Aminullah assagaf financial management p1621_ch. 16 sd 21_28 mei 2021
Aminullah assagaf financial management p1621_ch. 16 sd 21_28 mei 2021
Aminullah Assagaf31 visualizações
Aminullah assagaf p1621 ch. 16 sd 21_financial management_28 mei 2021 por Aminullah Assagaf
Aminullah assagaf p1621 ch. 16 sd 21_financial management_28 mei 2021Aminullah assagaf p1621 ch. 16 sd 21_financial management_28 mei 2021
Aminullah assagaf p1621 ch. 16 sd 21_financial management_28 mei 2021
Aminullah Assagaf13 visualizações
ch14- LONG TERM LIABILITIES.ppt por morium2
ch14- LONG TERM LIABILITIES.pptch14- LONG TERM LIABILITIES.ppt
ch14- LONG TERM LIABILITIES.ppt
morium224 visualizações
L3 - With Answers.pdf por newton47
L3 - With Answers.pdfL3 - With Answers.pdf
L3 - With Answers.pdf
newton475 visualizações
chapter5bondvaluationwithoutwrite-ups-121005143708-phpapp02.pdf por adnankhan765563
chapter5bondvaluationwithoutwrite-ups-121005143708-phpapp02.pdfchapter5bondvaluationwithoutwrite-ups-121005143708-phpapp02.pdf
chapter5bondvaluationwithoutwrite-ups-121005143708-phpapp02.pdf
adnankhan76556313 visualizações
FM_Chapter6.pdf por Sunny429247
FM_Chapter6.pdfFM_Chapter6.pdf
FM_Chapter6.pdf
Sunny429247103 visualizações
Time Value of Money I.pdf por swati23502
Time Value of Money I.pdfTime Value of Money I.pdf
Time Value of Money I.pdf
swati2350261 visualizações
3 aminullah assagaf ch. 16 sd 21_financial management_22 okt 2020 por Aminullah Assagaf
3 aminullah assagaf ch. 16 sd 21_financial management_22 okt 20203 aminullah assagaf ch. 16 sd 21_financial management_22 okt 2020
3 aminullah assagaf ch. 16 sd 21_financial management_22 okt 2020
Aminullah Assagaf110 visualizações
Financing current assets ppt @ bec doms bagalkot mba finanece por Babasab Patil
Financing current assets ppt @ bec doms bagalkot mba finaneceFinancing current assets ppt @ bec doms bagalkot mba finanece
Financing current assets ppt @ bec doms bagalkot mba finanece
Babasab Patil1.9K visualizações
nossi ch 13 updated por lesaturner
nossi ch 13 updatednossi ch 13 updated
nossi ch 13 updated
lesaturner422 visualizações

Mais de Chhavi Verma

Indian ethos, need, purpose por
Indian ethos, need, purposeIndian ethos, need, purpose
Indian ethos, need, purposeChhavi Verma
53.6K visualizações15 slides
Divya report por
Divya reportDivya report
Divya reportChhavi Verma
3.5K visualizações135 slides
“Impact of celebrity endorsement on brand equity of pepsi” por
“Impact of celebrity endorsement on brand equity of pepsi”“Impact of celebrity endorsement on brand equity of pepsi”
“Impact of celebrity endorsement on brand equity of pepsi”Chhavi Verma
17.8K visualizações112 slides
Ppt to jaipur dairy por
Ppt to jaipur dairyPpt to jaipur dairy
Ppt to jaipur dairyChhavi Verma
9.7K visualizações15 slides
Fsd ppt por
Fsd pptFsd ppt
Fsd pptChhavi Verma
846 visualizações11 slides
Report on home loan por
Report on home loanReport on home loan
Report on home loanChhavi Verma
2.3K visualizações26 slides

Mais de Chhavi Verma(6)

Indian ethos, need, purpose por Chhavi Verma
Indian ethos, need, purposeIndian ethos, need, purpose
Indian ethos, need, purpose
Chhavi Verma53.6K visualizações
Divya report por Chhavi Verma
Divya reportDivya report
Divya report
Chhavi Verma3.5K visualizações
“Impact of celebrity endorsement on brand equity of pepsi” por Chhavi Verma
“Impact of celebrity endorsement on brand equity of pepsi”“Impact of celebrity endorsement on brand equity of pepsi”
“Impact of celebrity endorsement on brand equity of pepsi”
Chhavi Verma17.8K visualizações
Ppt to jaipur dairy por Chhavi Verma
Ppt to jaipur dairyPpt to jaipur dairy
Ppt to jaipur dairy
Chhavi Verma9.7K visualizações
Fsd ppt por Chhavi Verma
Fsd pptFsd ppt
Fsd ppt
Chhavi Verma846 visualizações
Report on home loan por Chhavi Verma
Report on home loanReport on home loan
Report on home loan
Chhavi Verma2.3K visualizações

Último

Rangell Auto Detailing por
Rangell Auto Detailing Rangell Auto Detailing
Rangell Auto Detailing rangellautodetailing
12 visualizações8 slides
See the new MTN tariffs effected November 28, 2023 por
See the new MTN tariffs effected November 28, 2023See the new MTN tariffs effected November 28, 2023
See the new MTN tariffs effected November 28, 2023Kweku Zurek
29.4K visualizações2 slides
The 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdf por
The 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdfThe 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdf
The 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdfciolook1
6 visualizações32 slides
India's Leading Cyber Security Companies to Watch.pdf por
India's Leading Cyber Security Companies to Watch.pdfIndia's Leading Cyber Security Companies to Watch.pdf
India's Leading Cyber Security Companies to Watch.pdfinsightssuccess2
8 visualizações40 slides
Top 10 IT Tasks Small Businesses Can Entrust to Offshore Professionals por
Top 10 IT Tasks Small Businesses Can Entrust to Offshore ProfessionalsTop 10 IT Tasks Small Businesses Can Entrust to Offshore Professionals
Top 10 IT Tasks Small Businesses Can Entrust to Offshore Professionalsaltafhsayyednimetler
12 visualizações14 slides
voice logger software aegis.pdf por
voice logger software aegis.pdfvoice logger software aegis.pdf
voice logger software aegis.pdfNirmal Sharma
23 visualizações1 slide

Último(20)

See the new MTN tariffs effected November 28, 2023 por Kweku Zurek
See the new MTN tariffs effected November 28, 2023See the new MTN tariffs effected November 28, 2023
See the new MTN tariffs effected November 28, 2023
Kweku Zurek29.4K visualizações
The 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdf por ciolook1
The 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdfThe 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdf
The 10 Most Iconic Leaders in Supply Chain 2023_compressed.pdf
ciolook16 visualizações
India's Leading Cyber Security Companies to Watch.pdf por insightssuccess2
India's Leading Cyber Security Companies to Watch.pdfIndia's Leading Cyber Security Companies to Watch.pdf
India's Leading Cyber Security Companies to Watch.pdf
insightssuccess28 visualizações
Top 10 IT Tasks Small Businesses Can Entrust to Offshore Professionals por altafhsayyednimetler
Top 10 IT Tasks Small Businesses Can Entrust to Offshore ProfessionalsTop 10 IT Tasks Small Businesses Can Entrust to Offshore Professionals
Top 10 IT Tasks Small Businesses Can Entrust to Offshore Professionals
altafhsayyednimetler12 visualizações
voice logger software aegis.pdf por Nirmal Sharma
voice logger software aegis.pdfvoice logger software aegis.pdf
voice logger software aegis.pdf
Nirmal Sharma23 visualizações
SUGAR cosmetics ppt por shafrinn5
SUGAR cosmetics pptSUGAR cosmetics ppt
SUGAR cosmetics ppt
shafrinn536 visualizações
Businesses to Start in 2024.pdf por Dante St James
Businesses to Start in 2024.pdfBusinesses to Start in 2024.pdf
Businesses to Start in 2024.pdf
Dante St James16 visualizações
NYKAA PPT .pptx por 125071081
NYKAA PPT .pptxNYKAA PPT .pptx
NYKAA PPT .pptx
12507108110 visualizações
valuation firm. por NandniDhyani
valuation firm.valuation firm.
valuation firm.
NandniDhyani15 visualizações
AIR FRESHENER SUPPLIERS IN MUSCAT OMAN por Hygienelinks2
AIR FRESHENER SUPPLIERS IN MUSCAT OMANAIR FRESHENER SUPPLIERS IN MUSCAT OMAN
AIR FRESHENER SUPPLIERS IN MUSCAT OMAN
Hygienelinks28 visualizações
Effective Supervisory Skill por Seta Wicaksana
Effective Supervisory SkillEffective Supervisory Skill
Effective Supervisory Skill
Seta Wicaksana14 visualizações
ZARA.pptx por merlinjenma529
ZARA.pptxZARA.pptx
ZARA.pptx
merlinjenma52923 visualizações
Coomes Consulting Business Profile por Chris Coomes
Coomes Consulting Business ProfileCoomes Consulting Business Profile
Coomes Consulting Business Profile
Chris Coomes44 visualizações
PMU Launch - Guaranteed Slides por pmulaunch
PMU Launch - Guaranteed SlidesPMU Launch - Guaranteed Slides
PMU Launch - Guaranteed Slides
pmulaunch14 visualizações
Bloomerang_Forecasting Your Fundraising Revenue 2024.pptx.pdf por Bloomerang
Bloomerang_Forecasting Your Fundraising Revenue 2024.pptx.pdfBloomerang_Forecasting Your Fundraising Revenue 2024.pptx.pdf
Bloomerang_Forecasting Your Fundraising Revenue 2024.pptx.pdf
Bloomerang95 visualizações
Why Networking Events Don't Work_ Why You Should Give Talks Instead por HarryRamsay1
Why Networking Events Don't Work_ Why You Should Give Talks Instead Why Networking Events Don't Work_ Why You Should Give Talks Instead
Why Networking Events Don't Work_ Why You Should Give Talks Instead
HarryRamsay17 visualizações
Forex secret por konghatatih
Forex secret Forex secret
Forex secret
konghatatih15 visualizações
UCA towards I5.0 OECD.pdf por APPAU_Ukraine
UCA towards I5.0 OECD.pdfUCA towards I5.0 OECD.pdf
UCA towards I5.0 OECD.pdf
APPAU_Ukraine7 visualizações

Loans (1)

  • 1. TYPES OF LOANS • PURE DISCOUNT • INTEREST ONLY • CONSTANT PAYMENT
  • 2. TYPES OF LOANS PURE DISCOUNT LOANS PURE DISCOUNT LOANS: the borrower receives the money today and repays the loan in one lump sum at some time in the future. Example: you borrow $10,000 today and agree to repay the loan with 9% annual interest (compounded annually) five years from today. What is your loan balance in five years? FV = $10,000 (1 + 0.09)5 = $15,386.24
  • 3. TYPES OF LOANS PURE DISCOUNT LOANS Another example: Treasury Bills -- for historical reasons, the interest rate on a T-Bill is quoted as a discount: interest rate quoted = interest paid/par value. For example, the quoted rate on a one year $10,000 T-Bill at 7% interest is: Par value $10,000.00 Present value $ 9,345.79 Interest paid $ 654.21 The interest rate quoted is $654.21/$10,000 = 6.54% (even though the interest rate is 7%).
  • 4. TYPES OF LOANS INTEREST ONLY LOANS INTEREST ONLY LOAN: the borrower receives the money today and agrees to pay the lender interest periodically over the loan term and the principal (the original loan amount) at the end of the loan term. Example: you borrow $10,000 today and agree to pay interest annually at the annual rate of 9% and repay the principal at the end of five years. What is your annual interest payment? Interest = 0.09 x $10,000 = $900
  • 5. TYPES OF LOANS CONSTANT PAYMENT LOANS • • • • FIXED RATE OF INTEREST FIXED LOAN TERM FULLY AMORTIZING FIXED PERIODIC PAYMENTS
  • 6. TYPES OF LOANS CONSTANT PAYMENT LOANS Computing the equal periodic payment for amortized loans: PMT = Loan Amount where CR n k PMT = = = = 1 nk 1 ∑1 CR t t = (1 + ) k the annual contract rate of interest the number of years in the loan term the number of payments per year the equal periodic payment necessary to fully amortize the Loan Amount with nk payments.
  • 7. TYPES OF LOANS CONSTANT PAYMENT LOANS Compute the monthly payment necessary to fully amortize a 30 year, 8% annual interest (compounded monthly), $100,000 loan. PMT = $100,000 = 360 1 ∑ 0.08 t t = (1 + 1 ) 12 Annual debt service (DS) $ 733.76 = 12 x PMT = $8,805.12
  • 8. TYPES OF LOANS CONSTANT PAYMENT LOANS For a fixed rate, fixed term, fixed payment, fully amortizing loan, the mortgage balance (book value of the loan) is simply the present value of the remaining stream of payments discounted at the periodic contract rate. Let MBs = mortgage balance at the end of period s = PMT nk −s 1 ∑ CR t t = (1 + 1 ) k
  • 9. TYPES OF LOANS CONSTANT PAYMENT LOANS What is the mortgage balance in five years for a $100,000, 30 year, 8% annual interest rate, monthly payment loan? The mortgage balance in five years is the present value of the 300 (360-60) remaining monthly payments discounted at the monthly rate of 0.08/12. 300 MB60 1 = $733.76 ∑ = $ 95,069.26 0.08 t t = (1 + 1 ) 12
  • 10. TYPES OF LOANS CONSTANT PAYMENT LOANS Alternatively, the mortgage balance is the future value (FV) in: s 1 MBs PV = PMT ∑ + CR t CR s t =1 (1 + ) (1 + ) k k 60 1 MBs $100,000 = $733.76∑ + 0.08 t 0.08 60 t =1 (1 + ) (1 + ) 12 12
  • 11. TYPES OF LOANS CONSTANT PAYMENT LOANS Amortization schedules separate the periodic payment into interest and principal: Periodic interest payment = beginning balance x periodic rate or Is = MBs-1 Periodic principal CR k = periodic payment - periodic interest or Ps = PMT - Is
  • 12. TYPES OF LOANS CONSTANT PAYMENT LOANS Separate the $733.76 monthly payment into interest and principal for the first two months of the $100,000, 30 year, 8% annual interest rate loan. Month 1: Interest = $100,000.00 x 0.0066667 = $666.67 Principal = $733.76 - $666.67 = $ 67.09 MB1 = $100,000.00 - $67.09 = $99,932.91 Month 2: Interest = $99,932.91 x 0.0066667 = $666.22 Principal = $733.76 - $666.22 = $ 67.54 MB2 = $99,932.91 - $ 67.54 = $99,865.37
  • 13. TYPES OF LOANS CONSTANT PAYMENT LOANS How would you calculate the amount of interest you paid during the fifth year of a conventional mortgage? You could separate the monthly payments into interest and principal for the 12 months of the fifth year and add the monthly interest payments. Fortunately, there’s an easier way: Principal paid between months s and t = MBs - MBt Interest paid = PMT (t - s) - Principal paid
  • 14. TYPES OF LOANS CONSTANT PAYMENT LOANS Compute the principal and interest paid during the fifth year of a $100,000, 30 year, 8% annual rate, monthly payment mortgage. 312 MB48 1 = $733.76 ∑ 0.08 t t = (1 + 1 ) 12 = $96,218.44 300 MB60 = $733.76 1 ∑ 0.08 t t = (1 + 1 ) 12 = $95,069.26 Year 5: Principal paid: $96,218.44 - $95,069.26 = $1,149.17 Interest paid: $733.76 x 12 - $1,149.17 = $7,655.95
  • 15. TYPES OF LOANS CONSTANT PAYMENT LOANS In what month is one half of the loan repaid? s 1 $50,000 $100,000 = $733.76∑ + 0.08 t .08 s t = 1 (1 + ) (1 + ) 12 12 s = 269 (the 5th month of year 22)
  • 16. Constant Payment Mortgages: Yields The lender’s expected yield or borrower’s true borrowing cost is the IRR on the expected mortgage cash flows. Let Fee = loan origination fee, Points = discount points in dollars (points are usually expressed as a percent of the loan amount), S = month that the loan is repaid, PP = the dollar amount of the prepayment penalty (a percent of the mortgage balance), NLA = net loan amount = Loan Amount - Fee - Points y = the discount rate -- the lender’s yield, the borrower’s borrowing cost.
  • 17. Constant Payment Mortgages: Yields Computing Lender’s Yield (or Borrower’s Borrowing Cost) There are 3 cases to consider: (1) The loan is held to maturity; (2) the loan is repaid prior to maturity without penalty; (3) the loan is repaid prior to maturity with a prepayment penalty.
  • 18. Constant Payment Mortgages: Yields Computing Lender’s Yield (or Borrower’s Borrowing Cost) 1) If the loan is held to maturity, solve for y in: nk 1 NLA = PMT ∑ t t =1 (1 + y / 12 )
  • 19. Constant Payment Mortgages: Yields Example: compute the lender’s expected yield (or the borrower’s borrowing cost) for a $100,000, 30 year, monthly payment mortgage that has a 7.5% annual contract rate of interest if the lender charges a $1,000 loan origination fee, 2 discount points, and expects the borrower to hold the loan to maturity. NLA = $100,000 - $1,000 - $2,000 PMT = 360 = $97,000.00 1 = $100,000 / ∑ 0.075 t t = (1 + 1 ) 12 $699.21
  • 20. Constant Payment Mortgages: Yields Example (continued): the lender’s expected yield (or the borrower’s true borrowing cost) is the IRR (or discount rate y) in the following: 360 1 t =1 y t (1 + ) 12 $97,000 = $699.21∑ y = 7.81%
  • 21. Constant Payment Mortgages: Yields Computing Lender’s Yield (or Borrower’s Borrowing Cost) (2) If the loan is repaid prior to maturity without penalty, solve for y in: s 1 MBS NLA = PMT ∑ + y t y s t =1 (1 + ) (1 + ) 12 12
  • 22. Constant Payment Mortgages: Yields Example: compute the lender’s expected yield (or borrower’s borrowing cost) in the previous example if the lender expects the borrower to repay the loan, without penalty, at the end of four years. 312 1 MB48 = $699.21∑ = $95,860.00 0.075 t t =1 (1 + ) 12 Solve for y = 8.40% in: 48 1 $95,860.00 $97,000 = $699.21∑ + y t y 48 t =1 (1 + ) (1 + ) 12 12
  • 23. Constant Payment Mortgages: Yields Computing Lender’s Yield (or Borrower’s Borrowing Cost) (3) If the loan is repaid prior to maturity with a prepayment penalty, solve for y in: MBS + PPS NLA = PMT ∑ + y t y s t = 1 (1 + ) (1 + ) 12 12 s 1 Prepayment penalties are computed as a percent of the outstanding mortgage balance.
  • 24. Constant Payment Mortgages: Yields Example: compute the lender’s expected yield (or borrower’s borrowing cost) in the previous example if the lender expects the borrower to repay the loan, with a 2% prepayment penalty, at the end of four years. $95,860.00 + $1,917.20 $97,000 = $699.21∑ + y t y 48 t = 1 (1 + ) (1 + ) 12 12 48 1 FV = $97,777.20 and y = 8.82%
  • 25. Constant Payment Mortgages: Yields Relationship between mortgage yields and prepayment (with no prepayment penalty) for a 7.5%, 30 year, constant payment mortgage with a $1,000 loan fee and 2 discount points. Year of Prepayment 1 2 3 4 5 10 20 30 Mortgage Yield 10.69% 9.16% 8.65% 8.40% 8.25% 7.96% 7.83% 7.81%
  • 26. Constant Payment Mortgages: Yields The Annual Percentage Rate (APR) on a loan is the lender’s yield (or borrower’s borrowing cost) computed assuming the loan is held to maturity rounded to the nearest one-eighth. The APR for the loan in the previous example is 7 3 . 4
  • 27. Constant Payment Mortgages: Yields Charging Points to Achieve a Desired Yield If a lender has a required yield of y, then the points the lender must charge to obtain the required yield are computed by solving for ‘Points’ in: MB s + PPs 1 Loan Amount − Points − Fee = PMT∑ + y y t =1 (1 + ) t (1 + ) s 12 12 s
  • 28. Constant Payment Mortgages: Yields Example: compute the points a lender must charge to earn a 9% required yield on a $100,000, 30 year, 7.5% annual interest rate, monthly payment mortgage if the lender charges a $1,000 loan origination fee and expects the borrower to repay the loan, without penalty, at the end of four years. 48 1 $95,860.00 $100,000 − Points − $1,000 = $699.21∑ + 0.09 t 0.09 48 t= 1 (1 + ) (1 + ) 12 12 $99,000 - Points = $95,066.75; Points = $3,933.25
  • 29. Alternative Mortgage Instruments • Graduated Payment Mortgages (GPMs) • Price Level Adjusted Mortgages (PLAMs) • Adjustable Rate Mortgages (ARMs) • Reverse Annuity Mortgages (RAMs) • Shared Appreciation Mortgages (SAMs)
  • 30. Alternative Mortgage Instruments Graduated Payment Mortgage Fixed • Contract Rate Fixed • Loan Term Payments Increase During First Few Years • Payments Known in Advance • Permit • Negative Amortization
  • 31. Alternative Mortgage Instruments Graduated Payment Mortgage Loan Rate Term = = = $100,000 12% 30 years with monthly payments; payment increases 7.5% per year for first five years Year 1 2 3 4 5 6-30 Monthly Payment $ 791.38 850.73 914.54 983.13 1,056.86 1,136.13 Monthly Interest $ 1,000.00 1,026.46 1,048.75 1,065.77 1,076.25 Ending Balance $ 102,645.82 104,874.52 106,576.64 107,624.72 107,870.63
  • 32. Alternative Mortgage Instruments Price Level Adjusted Mortgage For a fixed payment mortgage, the contract rate of interest, CR, is: CR = rf + ρ + inf where rf = risk free rate = ρ risk premium inf = expected inflation rate With a Price Level Adjusted Mortgage (PLAM), CR = rf + ρ and the outstanding mortgage balance is indexed to the price level to compensate the lender for inflation.
  • 33. Alternative Mortgage Instruments Price Level Adjusted Mortgage Loan Rate Term Inf = = = = Year 1 2 3 $100,000 5% 30 years with monthly payments 5%, 6%, and 4% Beginning Balance $ 100,000.00 103,450.55 107,931.31 Monthly Payment $ 536.82 563.66 597.48 Ending Balance Before After $ 98,524.34 $ 103,450.55 101,821.99 107,931.31 106,116.98 110,361.66
  • 34. Alternative Mortgage Instruments Adjustable Rate Mortgages Contract • Rate Indexed to Lender’s Cost of Funds (plus a margin) Term •May Adjust Monthly • Payment May Adjust Negative • Amortization May be Permitted Typically Have Periodic and Lifetime Interest Rate Caps •
  • 35. Alternative Mortgage Instruments Adjustable Rate Mortgages Loan Initial Rate Term Index Margin Caps Year 1 2 3 = = = = = = $100,000 9% 30 years with monthly payments Yields on 1-Year Treasury Securities ( 8%, 9%, 7%) 2.5% 2/5—200bp annual cap and 500bp lifetime cap Beginning Balance $ 100,000.00 99,316.84 98,815.85 Interest Rates Market Contract 9.0% 9.0% 11.5% 11.0% 9.5% 9.5% Monthly Payment $ 804.62 950.09 841.79
  • 36. Alternative Mortgage Instruments Reverse Annuity Mortgages The borrower: receives the loan in periodic installments • repays the loan in one lump sum at the end of the term • The monthly RAM receipt on a 10 year, $50,000, 8% annual interest rate RAM is $273.30. The borrower will recieve 120 of these monthly payments. At the end of the loan term, the borrower will repay the lender $50,000. Principal = 120 x $ 273.30 = $ 32,796.56 Interest = $50,000 - 32,796.56 = $ 17,203.44
  • 37. Alternative Mortgage Instruments Shared Appreciation Mortgages The lender provides the borrower with: a below • market rate of interest, or cash •to pay a portion of the down payment, or both • In exchange for a share of the property value appreciation during the hoding period.