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	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:

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.

Posted Date: 4/9/2013 2:24:15 AM | Location : United States

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