Mr Smith plans to invest his money in unit trust with a bank. His target is to earn an interest of $10,000 after 5 years. The bank pays 3% compound interest per annum compounded yearly. Calculate, to the nearest hundred dollars, the minimum amount of money Mr Smith has to invest. Answer $___

1. Set up the compound interest relationship for the amount after 5 years

Let the amount invested be $P.

After 5 years at 3% compound interest per annum,
$\text{final amount}=P(1.03)^5.$

2. Use the fact that the interest earned is \$10 000

Interest earned = final amount $-$ principal.

$P(1.03)^5-P=10000$
$P\left((1.03)^5-1\right)=10000$

3. Solve for the principal and round to the nearest hundred dollars

$P=\frac{10000}{(1.03)^5-1}$
$P=62784.85\ldots$

To the nearest hundred dollars,
$P=62800.$