1. MATHEMATICS OF FINANCE
INTEREST:
> Is a fraction or percentage being imputed to a sum of
money.
SIMPLE INTEREST:
> Is essentially the interest charged to a borrower or
earned by a lender for the full term of the loan.
2. • FORMULA:
I = P x R x T
Where:
I = interest
P = Principal
R = Rate
T = time
3. • TIME CONVERSION:
• > IF THE TIME IS IN TERMS OF:
• MONTHS, DIVIDE BY 12.
• SEMIANNUALLY, DIVIDE BY 2.
• QUARTERLY, DIVIDE BY 4.
• SEMIMONTHLY, DIVIDE BY 24.
• > IF THE TIME IS EXPRESSED IN DAYS:
• EXACT INTEREST: t = number of days/ 365
• ORDINARY INTEREST: t =number of days/ 360
4. PRINCIPAL : The sum of money that
someone borrows.
RATE : is a percentage of the principal
amount.
TIME: is the agreed date or period when the
loan will be paid in full.
5. • 1. Given:
• P = P10,000
• R= 5 % per month
• Time = 5 months
• I = ?
• 2. Given:
• I = P 6,000
• P = P 20,000
• R = 8% per year
• T = ?
3. Given:
R = 15% per month
Time = 6 months
I = P 4,500
P = ?
4. Given:
P = P 30,000.
I = P 9,000.
R = ? ( per month)
T = 3 months
6. MATURITY AMOUNT OR FINAL
AMOUNT: ( for simple interest)
Is the amount to be paid to the holder of a
financial obligation at the obligation’s
maturity.
FINAL AMOUNT FORMULA:
F = P + I
or
F = P ( 1 + rt) r = F – P/ Pt
t = F –P/ Pr
7. 1. GIVEN:
P = 100,000
R = 8% per annum
T = 5 years
I = ?
F = ?
2. GIVEN:
F= P 200,000
P = P 100,000
T = 7 years
R = ?
8. COMPOUND INTEREST:
Is similar to simple interest, only
that the interest charged or
earned is being rolled – up and
reinvested with the principal
amount.
The sum by which the original
principal has increased by the end
of the term of the investment.
9. The conversion period it can be:
• Quarterly ( 4 periods)
• Semiannually( 2 periods)
• Monthly ( 12 months)
10. FORMULA:
n
F = P( 1 + i)
Where:
F=Maturity amount
P = Principal amount
i = Interest rate per conversion( expressed as decimal )
i = j / m j : annual rate , m = number of conversion
periods per year
n= number of conversion periods
11. • Example 1.
Accumulate P 5,000 for 3 years at 10%
compounded quarterly.
Given:
P = P5,000
n=3(4) = 12
i = j/m = 10%/ 4 = .10/4 = 0.025
12. • Example 2
• Find the amount due at the end of 6 ¾ years
if P 2,000 is invested at 12% compounded
monthly.
• Given:
• i=j /m = .12/ 12 = .01
• P = p2,000
• n=12(6 ¾) =81
13. • MATURITY AMOUNT in Compound amount
• Formula:
-n
M = F ( 1 + I ) or
F
=
n
( 1 + i)
Where:
M = Maturity amount
14. • 1. Find the maturity amount of p5,000 due in
6 years if money is worth 12% compounded
semiannually.
• 2. If money can be invested at 12%
compounded semiannually, find the maturity
amount of p1,000 due at the end of 5 ½
years.
