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Express Lane Plus
Posts: 252
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4 days 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.) Read 30 times 1 Reply
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wrote...
Educator
4 days 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$$i=\frac{0.04}{12}=\frac{1}{300}$$$$n=3\cdot 12=36$$ periodsAmount 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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