Mrs Tan planned to earn an interest of $1000 at the end of 5 years by investing her money in a bank. The rate of compound interest was fixed at 1.25% per annum. Find the amount of money she needed to deposit in the bank. Answer $ ...

1. Form the compound amount and interest in terms of the principal

Let the amount deposited be $P.

After 5 years,
$\text{Amount}=P\left(1+\frac{1.25}{100}\right)^5=P(1.0125)^5.$

The interest earned is
$P(1.0125)^5-P.$

2. Set up and solve the equation for the required deposit

Since the interest earned is $1000,
$P(1.0125)^5-P=1000$
$P\left[(1.0125)^5-1\right]=1000$
$P=\frac{1000}{(1.0125)^5-1}.$

3. Evaluate and round the money value appropriately

$P=\frac{1000}{1.0640821536-1}$
$P=15604.96\ldots$

So the amount she needed to deposit was
$\$15604.97 \text{ correct to the nearest cent}.$