THE TIME VALUE OF MONEY

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THE TIME VALUE OF MONEY
DR. AHMET TEZEL
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Time Value of Money
Present Value of Single Sum PVIF(i,n)
Present Value of Annuity PVIFA (i,n)
Future Value of Single Sum FVIF (i,n)
Future Value of Annuity FVIFA (i,n)
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Future Value
0____________1____________2______________
3 PV1,000 1,100
1,210 FV3 1,331 PV Present
value FV Future value i Interest rate n
Number of periods FVn PV(1i)n
PV(FVIF i,n) FV3 1,000(1.1)3
1,000(1.331) 1,331 Question What is the
future value of 5,000 in 10 years at a 10 percent
annual rate?
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Future Value of 1
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Chart Future Value of 1
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Present Value
0____________1____________2______________
3 PV1,000 1,100
1,210 FV3 1,331 PV Present
value FV Future value i Interest rate n
Number of periods PV FV /
(1i)n FV(PVIF i,n) PV 1,331 /
(1.1)3 1,331(0.7513) 1,000 Question What
is the present value of 8,000 in 10 years at a 15
percent annual rate?
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Present Value of 1
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Chart Present Value of 1
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Future Value of an Annuity
0_________1_________2____________3__________ 4
PMT100 100
100 100 PMT Periodic payments
100(1.10)

100(1.10)2

100(1.10)3 FVA4 100100(1.10)100(1.
10)2 100(1.10)3 464.10 FVA n PMT (1i)n -1
/ i PMT(FVIFA i,n)100(4.641)
FVA(1i)n 1 / i
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Sinking Fund Example
To accumulate 1 million in 30 years, how much do
you have to save and invest at the end of each
year if you earn a 9 annual return ?
1,000,000 PMT(FVIFA 9, 30) PMT(136.31)
PMT 1,000,000 / 136.31 7,336.22 If you earn
12, PMT1,000,000/241.33 4,143.71
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Present Value of an Annuity
0_________1_________2____________3__________ 4
PMT100 100
100 100
100/(1.10) 100/(1.10)2
100/(1.10)3 100/(1.10)4 PVA4
1001/(1.10) 1/(1.10)21/(1.10)3 1/(1.10)4
317 PVA n PMT 1-1/(1i)n / i PMT(PVIFA
i,n)100(3.170) If n20 years, PVA 100(8.5136)
851.36 Perpetuity If n approaches infinity,
PVAPMT / i 100/ 0.1 1,000
PVA 1-1/(1i)n / i
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Loan Amortization Table
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Effective Annual Rate EAR
EAR (1simple i/m)m -1 where m is the
frequency of compounding. Credit Card with
monthly compounding(1 a month)
EAR(10.01)12 -1 0.12682512.6825 Bank Loan
with quarterly compounding(3 per quarter)
EAR(10.03)4 -1 0.12550912.5509
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EAR for maturity less than one year
Discount yield ((Face value-Discount
price)/Face Value) (360/maturity in days) Bond
equivalent yield ((Face value-Discount
price)/Discount price) (365/maturity in days)