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.

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 × 1/(1 + r)ⁿ
= $20,000 × 1/(1 + 10%)¹⁵
= $20,000 × 0.239*
= $4,780

 *Value of 1/(1 + 10%)¹⁵ from present value of $1 table: 15 periods; 10%.

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 × 1/(1 + r)ⁿ
= $20,000 × 1/(1 + 14%)¹⁵
= $20,000 × 0.140*
=$2,800

 *Value of 1/(1 + 14%)¹⁵ from present value of $1 table: 15 periods; 14% interest rate.

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