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Express Lane Plus
Posts: 351
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2 months ago
Find the final amount in the following retirement account, in which the rate of return on the account and the regular contribution change over time. $596 per month invested at 4%, compounded monthly, for 3 years; then $738 per month invested at 5%, compounded monthly, for 3 years.
What is the amount in the account after 6 years?
$?  
(Do not round until the final answer. Then round to the nearest dollar as needed.)
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Educator
2 months ago
Let's begin with the first 3 years

\( 4%\) to decimal \(\rightarrow \ 0.04\)

Because it's compounded monthly, divide \(i\) by 12 and multiply \(n\) by 12

\(i=\frac{0.04}{12}=\frac{1}{300}\)

\(n=3\cdot 12=36\) periods

Amount after 3 years = \(\frac{596\left[(1+i)^{36}-1\right]}{i}\)

Substitute what \(i\) is equal to:

\(\frac{596\left[\left(1+\frac{1}{300}\right)^{36}-1\right]}{\frac{1}{300}}=22756.211\)

Let's continue now with the last 3 years

\(\frac{738\left[\left(1+\frac{0.05}{12}\right)^{36}-1\right]}{\frac{0.05}{12}}=28599.961\)

Lastly, you sum up: \(22756.211 + 28599.961\) and round = 51356.17
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