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Find the final amount in the following retirement account, in which the rate of return on the accoun
Catracho
Catracho
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5 months ago
Find the final amount in the following retirement account, in which the rate of return on the accoun
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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bio_man
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#1
Educator
5 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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