Exercise-2: Computation of present value of a single sum

Learning objective:
This exercise illustrates the computation of present value of a single sum that will be received on a predetermined future date. It also highlights the impact of change in interest rate on the present value of a single sum to be received in future.

An employee plans to retire in 15 years. After retirement, he will need an amount of $20,000 to start a small business.

Required: Compute the amount that the employee needs to invest today to have $20,000 upon his retirement assuming an interest rate of:

1. 10% compounded annually.
2. 14% compounded annually.

Solution:

(1) Investment required at 10% interest rate:

PV = FV × PVIF_{i%, n}
= $20,000 × PVI_{10%, 15}
= $20,000 × 0.239*
= $4,780

*Value from present value of $1 table:
10% interest rate, 15th period

At 10% interest rate, the employee needs to invest $4,780 today to have an amount of $20,000 after 15 years.

(2) Investment required at 14% interest rate:

PV = FV × PVIF_{i%, n}
= $20,000 × PVIF_{14%, 15}
= $20,000 × 0.140*
=$2,800

*Value from present value of $1 table:
14% interest rate, 15th period

At 14% interest rate, the employee needs to invest $2,800 today to have an amount of $20,000 after 15 years.

Notice that an increase of interest rate from 10% to 14% has decreased the present value of $20,000 amount from $4,780 to $2,800. Students should remember that when interest rate increases, the present value of the same amount decrease, and vice versa.