Title: Find the final amount in the following retirement account, in which the rate of return on the accoun Post by: Catracho on Dec 7, 2018 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.) Title: Re: Find the final amount in the following retirement account, in which the rate of return on the ... Post by: bio_man on Dec 7, 2018 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 |