Compute the future value of Rs.5000 at the end of 6 years, whether nominal interest rate is 12 percent and the interest is allocated (payable) quarterly at frequency = 4
Solution:
FV_{n} = PV (1 + k/m )^{m*}^{n}
FV_{6} = 5000(1 + .12/4)^{6*4}
= 50000 (1 + .03)^{24}
= 5000 * 2.0328
= 10,164
After 6 years the future value of Rs.5000 on the origin of quarterly compounding would be as Rs.10 164 whereas in condition of semi-annual and yearly compounding the future value would be as
FV_{6} = 5000(1 + .12/2)^{6*2}
= 50000 (1 + .06)1^{2}
= 5000 * 2.0122
= 10,061
FV_{6} = 5000(1 + .12)^{6}
= 5000(1.9738)
= 9868
This dissimilarity in future value is because of the fact that interest on interest has been computed.