Question

$75,000 is invested at 5% compounded annually. Find the total amount, to the nearest cent, after 5 years.

$0.02

$58,033.57

$569,531.25

$95, 7521.12

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$75000\\ r=rate\to 5\%\to (5)/(100)\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &5 \end{cases} \\\\\\ A=75000\left(1+(0.05)/(1)\right)^(1\cdot 5)\implies A=75000(1.05)^5`

Answer 2

For purposes of this multiple-choice question, you know the result will be more than $75,000, so the first two choices are ruled out immediately.

The doubling time of the amount is (roughly) 72/(interest rate%) = 72/5 = 14.4 years, so you know the amount will not be doubled (to $150,000) in only 5 years.

The only viable choice is the last one, $95,721.12.

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A little "number sense" goes a long way on multiple-choice questions.