Exercise-2 (Computation of present value of a single sum )

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 employee needs to invest today to have an amount of $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*

= $4780

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

(1) 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.