Let us assume that you deposit Rs.1000 in a bank that pays 10 percent interest compounded yearly for a period of 3 years. The deposit will grow as given details:
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First Year
|
Principal at the beginning. Interest for the year (1000x.10) Total amount
|
Rs.
1000
100
1100
|
|
Second Year
|
Principal at the beginning. Interest for the year (1100x.10). Total Amount
|
1100
110
1210
|
|
Third Year
|
Principal at the beginning. Interest for the year (1210x.10)
Total Amount
|
1210
121
1321
|
To acquire the future value from current value for one year period:
FV = PV + (PV . k)
Here PV = Present Value;
k = Interest rate
FV = PV (1 + k)
As the same for a two year period:
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FV = PV
|
+ (PV × k)
|
+ (PV × k)
|
+ (PV × k × k)
|
|
Principal amount
|
First period interest on principal
|
Second period interest on the principal
|
Second periods interest on the first periods interest
|
FV = PV+PVk+PVk+PVk2
= PV+2PVk+PVk2
= PV (1+2k+K2) = PV (1+k)2
Hence, the future value of amount after n periods is as:
FV = PV (1+k)n ............................Eq(1)
Here FV = Future value n years thus
PV = Cash today or present value
k = Interest rate par year in percentage
n = number of years for that compounding is done
Equation (1) is the fundamental equation for compounding analysis. Here the factor (1+k)n is considered as the future value interest factor or the compounding factor (FVIFk,n). Published tables are obtainable showing the value of (1+k)n for different combinations of k and n. In such table is specified in appendix A of this section.