Assume Mr. Ram deposits Rs. 10,000 annually in a bank for 5 years, at 10 percent compound interest rate. Compute the value of this series of deposits on the end of five years by assuming that (i) all deposit occurs on the end of the year (ii) all deposit occurs at the starting of the year.
Solution:
The future value of regular annuity will be as:
Rs. 1000 (1.10)4 + 1000 (1.10)3 +1000 (1.10)2+1000 (1.10) +1000
= 6105.
The future value of an annuity due will be as:
Rs. 1000 (1.10)5 + 1000 (1.10)4 +1000 (1.10)3+1000 (1.10)2 +1000 (1.10)
= Rs 1000 (1.611) + 1000 (1.4641) + 1000 (1.331) + 1000 (1.21)+1000 (1.10)
= Rs. 6716.
In the above illustration you have seen the dissimilarity in future value of a regular annuity and annuity due. This diversity in value is because of the timing of cash flow. Within the case of regular annuity, the last cash flow doesn't earn any interest, for individual period the cash flows earns an interest and in case when annuity due.