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Annual Compounding of a Series of Payments

Table 2.5

Annual Compounding of a Series of Payments

Column 3 of Table 2.5 indicates that since the deposits are made at the end of the year, the first deposit will earn interest for four years, the second for three years and so on. The last payment of Rs 2,500 comes at the end of the fifth year and, therefore, the future value remains Rs 2,500. The future value of the entire stream of payments is-the sum of the individual future values, that is, Rs 8,020.50. The graphic presentation of these values is shown in the following time scale diagram which shows the equivalence of money.

Graphic Illustration of Compounding Values.

Graphic Illustration of Compounding Values.

It may be noted here that we are making use of the compound interest formula for each payment separately. For instance, Rs 500 put in at the end of the first year compounds for four years, and has a future value of Rs 608 at 5 per. cent interest. Similarly, Rs.1.000 deposited at n = 2 compounds for 3 years and amounts to Rs 1,158 |Rs 1,000 (1 + 0.05)3| and so on.