The Process of Going Forward, From Present Values (PVS) To Future Values (FVS), Is Called Compounding
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sittoolwinThe Process of Going Forward, From Present Values (PVS) To Future Values (FVS), Is Called Compounding
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sittoolwinTime Value Of Money
Time Line
Years 0 1 2 3 4
5%
Cash PV = $ 100 FV = ?
Future Value
The process of going forward, from present values (PVs) to future values (FVs), is called
compounding.
FVn = PV (1 + i)n
𝐹𝑉𝑛
PV = ( 1+𝑖 )𝑛
Where FVn = Future Value
n = Number of Years
i = Interest Rate
pv = Present Value
Future Value Periodically
𝐹𝑉𝑛
PV = 𝑖 𝑛𝑚
(1+𝑚 )
𝑖
FVn = PV (1 + 𝑚)nm
Where;
m = number of period interest paid in annually
semi annual = 2 times
quarterly = 4 times
𝑛 𝐹𝑉𝑛
i = √ −1
𝑃𝑉
ANNUITIES
Ordinary Annuity
Period 0 1 2 3
Payment -$ 100 -$ 100 -$100
$ 100
$ 105
$ 110.25
$ 315.25
FV=PV(1 + i)n
(1+𝑖)𝑛 − 1
Future Value Annuity Ordinary 1. FVAn = PMT { }
𝑖
Annuity Due
Period 0 1 2 3
Payment -$ 100 -$ 100 -$100
$ 105
$ 110.25
$ 115.76
$ 331.01
FV=PV(1 + i)n
(1+𝑖)𝑛 − 1
Future Value Annuity DUE FVAn = PMT { } (1 + i )
𝑖
Ordinary Annuity
Period 0 1 2 3
Payment -$ 100 -$ 100 -$100
$ 92.24
$ 90.70
$ 86.38
$ 272.32
𝐹𝑉𝑛
PV = (1+𝑖)𝑛
1
1−(1+𝑖)𝑛
Present Value Annuity PVAn = PMT ( )
𝑖
Annuity Due
Period 0 1 2 3
Payment -$ 100 -$ 100 -$100
$ 100
$ 90.24
$ 90.70
𝐹𝑉𝑛
$ 285.94 PV = (1+𝑖)𝑛
1
1−(1+𝑖)𝑛
Present Value Annuity Due PVAn(Due) = PMT ( ) (1 + i )
𝑖
𝑖𝑁𝑜𝑚 𝑚
EAR (or EFF %) = (1 + ) − 1.0 Effective (or equivalent) annual rate (EAR)
𝑚