# Exercise-3 (Computation of present value of an annuity)

A woman will need an amount of $2,000 to go on vacations with her husband at the end of each year for 10 years. For this purpose she wants to invest some money in a saving bank but does not know the exact amount of money to invest.

**Require:** What amount does she require to invest now to receive an income of $2,000 at the end of each year for 10 years if:

- the interest rate is 15%
- the interest rate is 18%

## Solution:

Because woman needs equal amounts at the end of each year, it is an annuity and she needs to invest an amount that is equal to the present value of this annuity at given interest rate.

### (1) If the interest rate is 15%:

= $2,000 × [(1 + 15%)^{10} – 1/15%(1 + i)^{10}]

= $2,000 × 5.019*

= $10,038

*Value of [(1 + 15%)^{10} – 1/15%(1 + i)^{10}] from present value of an annuity of $1 in arrears table.

### (2) If the interest rate is 18%:

= $2,000 × [(1 + 18%)^{10} – 1/18%(1 + i)^{10}]

= $2,000 × 4.494*

= $8,988

*Value of [(1 + 18%)^{10} – 1/18%(1 + i)^{10}] from present value of an annuity of $1 in arrears table.

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