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show all of your work to arrive a final result Simple Interest Simple Interest, I = P *n * 1 I- Simple Interest P Principal (amount borrowed or lent) Final Amount, F P-P Pni n-number of interest periods i- simple interest rate Compound Interest Factors 1interest rate n = number of interest (compounding) periods P- present sum (initial principal amount) (F/P): Algebraic Notation: FP(1 i)\" A- an equal periodic amount (uniform series) F-a future sum (P/F): Algebraic Notation: P F(1 i) (A/F): Algebraic Notation: A F (AP): Algebraic Notation : A- (A/G): Algebraic Notation: G (P/G): Algebraic Notation: G2 Factor Notation: F - P(F/P i, n Factor Notation: P -F(P/F i,n A A(F/A i, n (F/A): Algebraic Notation: F Factor Notation: F Factor Notation: A-F(A/F i,n (P/A): Algebraic Notation: P A (P/A): Algebraic Notation: PAR Factor Notation: PA(P/A i,n Factor Notation: A -P(A/P i,n (NG): Factor Notation : A A1 ± G(A/G í, n) A1 Constant amount G-Gradient amount (P/G): Factor Notation: A1(P/A i,n)t G(P/G i, n) Interest Rate Conversion: 7 Effective Interest Rate, i - Effective Annual Interest rate, ( 1 + Nominal Interest Rate, rc(1 + i)c) - 1 Continuous Interest Factors: Pe\" PF/P i, n] (F/P): Algebraic Notation: F (P/F): Algebraic Notation: P- F (A/F): Algebraic Notation: A F (A/P): Algebraic Notation: A P Factor Notation: F Factor Notation: PFP/F i,n (F/A): Algebraic Notation: FAT (em-1) Factor Notation: F -A|F/A i,n Factor Notation: A- F[A/Fi,n (1 71 (P/A): Algebraic Notation: P-A Factor Notation: P A[P/A i, n Factor Notation: A = P [A/P i, n Solution In both the cases, the amount deposited in the bank (P) = $5000 and the time is 6 years. a) When the interest is compounded quarterly, the formula of the Amount (A) is: A = P{1+ (r/n)}nt where r is the interest rate, n is the number of times interest is compounded per year and t is the time in years. Here t=6 years, n= 4 and r = 12% p.a or 12/100 = 0.12. Therefore, A = 5000 (1+(0.12/4)4*6 A = $10,163.97 Thus the interest received when interest is compounded quarterly is $10163.97-$5000 = $5163.97 b) When the interest is compounded continuously, the formula of the Amount (A) is: A = P*ert where r is the interest rate and t is the time in years. For this example r = 10% or 10/100 = 0.10. Therefore, A = 5000*e(0.10*6) Or A = $9110.59 Therefore the interest received when interest is compounded continuously is $9110.59 - $5000 = $4110.59.
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10/31/19 1 EE 200: Engineering Economics 2 Time Value of Money 2 2 136 ENGINEERING ECONOMICS ENGINEERING ECONOMICS Factor Name Converts Symbol Formula Single Payment Compound Amount to F given P (F/P, i%, n) (1 + i) n Single Payment Present Worth to P given F (P/F, i%, n) (1 + i) –n Uniform Series Sinking Fund to A given F (A/F, i%, n) ( ) 11 + ni i Capital Recovery to A given P (A/P, i%, n) ( ) ( ) 11 1 + + n n i ii Uniform Series Compound Amount to F given A (F/A, i%, n) ( ) i i n 11 + Uniform Series Present Worth to P given A (P/A, i%, n) ( ) ( )n n ii i + + 1 11 Uniform Gradient Present Worth to P given G (P/G, i%, n) ( ) ( ) ( )nn n ii n ii i ++ + 11 11 2 Uniform Gradient † Future Worth to F given G (F/G, i%, n) ( ) i n i i n+ 2 11 Uniform Gradient Uniform Series to A given G (A/G, i%, n) ( ) 11 1 + ni n i NOMENCLATURE AND DEFINITIONS A �������������Uniform amount per interest period B �������������Benefit BV �����������Book value C �������������Cost d��������������In ation ad usted interest rate per interest period Dj ������������Depreciation in year j EV �����������Expected value F �������������Future worth, value, or amount f �������������� eneral in ation rate per interest period G �������������Uniform gradient amount per interest period i ��������������Interest rate per interest period ie �������������Annual effective interest rate MARR ����Minimum acceptable/attractive rate of return m �������������Number of compounding periods per year n��������������Number of compounding periods; or the expected life of an asset P �������������Present worth, value, or amount r ��������������Nominal annual interest rate Sn ������������Expected salvage value in year n Subscripts j ����������� at time j n����������� at time n †����������� F/G = (F/A – n)/i = (F/A) × (A/G) Risk Risk is the chance of an outcome other than what is planned to occur or expected in the analysis� NON-ANNUAL COMPOUNDING i m r1 1e m = + -b l BREAK-EVEN ANALYSIS By altering the value of any one of the variables in a situation, holding all of the other values constant, it is possible to find a value for that variable that makes the two alternatives equally economical� This value is the break-even point� Break-even analysis is used to describe the percentage of capacity of operation for a manufacturing plant at which income will ust cover expenses. The payback period is the period of time required for the profit or other benefits of an investment to equal the cost of the investment� Time Value of Money Relating Future and Present Worth Shows Unreasonable Costs 3 𝐹 is Future Worth 𝑃 is Present Worth 𝑛 is the number of compounding periods 𝐴 is Uniform Amount per interest period (Payment) 𝑖 is the interest rate per period 3 10/31/19 2 College Costs Have Historically Increased Faster than Inflation: Compound Interest Model • Umich: Total Annual Cost o 1980: $3,500 o 2020: $30,0
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Factors and their use
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ENGINEERING ECONOMY Factors
and their Use
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