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:
- 10% compounded annually.
- 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.
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