Assume you are receiving an amount of Rs.5000 twice in a year for subsequent five years one time at the starting of the year and another amount of Rs. 5000 at the ending of the year that you deposit in the bank that pays an interest of 12%. Calculate the value of the deposit at the ending of the fifth year.
Solution: In this type of problem we have to compute the future value of two annuities of Rs.5000 consisting duration of five years. The primary annuity is an annuity due and the next annuity is regular annuity, thus the value of the deposit at the ending of five year would be as:
FVA_{n} + FVA_{n(due)}
= A [((1 + k)^{n} - 1)/k] + A [((1 + k)^{n} - 1)/k](1 + k)
= A (FVIFA_{12, 5}) + A (FVIFA_{12, 5} ) (1 + k)
=5000 (6.353) + 5000 (6.353)(1.12)
= 31,765 + 35,577
=67336
The value of deposit at the ending of the fifth year = Rs. 67,342.