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

Posted in: Capital budgeting techniques (exercises)

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:

- 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*

= $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.

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