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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:
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
110
1210
Third Year
Principal at the beginning. Interest for the year (1210x.10)
Total Amount
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:
FV = PV
+ (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.
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