Determine out the future value of Rs.1000 compounded yearly for 10 years at an interest rate of 10 percent.
Solution: The future value 10 years thus would be
FV = PV (1+k)^{n}
FV = 1,000 (1+.10)^{10}
= 1000 . (1.10)^{10}
= 1000 (2.5937)
= 2593.7
The appreciation in current value of an amount can also be shown in terms of return. So the return is the income on investment over every period divided via the amount of investment in the starting of the period. By the above illustration the arithmetic average return would be (2593.7 -1000)/1000=159.37percent over the ten year period or 15.937 percent per year. The major problem of using arithmetic average is which it avoids the process of compounding. For overcome this, the accurate method is to use geometric average return to compute overage annual return.
Rearranging the equation 1 we find out that:
k = n ((√((FV)/(PV))) - 1) ................................Eq(2)
By using the values of Eq. 1
= 10 (√(2593.7/1,000) ) - 1
= ((2593.7/1,000)^{1/10}) - 1
= 1.10 - 1
= .10
= 10 %