史密斯先生计划将他的资金投资于某银行的单位信托。他的目标是在5年后获得 $10,000 的利息。该银行每年按 3% 的年复利计息。计算史密斯先生最少需要投资的金额，结果精确到最接近的一百美元。 答案 $___

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,
$P=62800.$