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Express Lane Plus
Posts: 256
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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.

$247 per month invested at 6%, compounded monthly, for 5 years; then $651 per month invested at %7, compounded monthly, for 5 years.
what is the amount in the account after 10 years?
​(Do not round until the final answer. Then round to the nearest dollar as​ needed.)
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wrote...
Educator
2 months ago
I think here you do the annuity thing twice, then add them:

\(A=\frac{R\left[\left(1+\frac{r}{n}\right)^t−1\right]}{\frac{r}{n}}\)

1st

A = future value amount
R = regular deposit/payment  \(\rightarrow\) 247
r = interest rate \(\rightarrow\) 6% or 0.06
n = compounding periods per year \(\rightarrow\) 12
t = total number of deposits \(\rightarrow\) 12 * 5 = 60

2nd

A = future value amount
R = regular deposit/payment  \(\rightarrow\) 651
r = interest rate \(\rightarrow\) 7% or 0.07
n = compounding periods per year \(\rightarrow\) 12
t = total number of deposits \(\rightarrow\) 12 * 5 = 60

\(A_T=\frac{247\left[\left(1+\frac{0.06}{12}\right)^{60}−1\right]}{\frac{0.06}{12}}+\frac{651\left[\left(1+\frac{0.07}{12}\right)^{60}−1\right]}{\frac{0.07}{12}}\)

\(A_T=17233.19754+46606.97897\)

\(A_T=63840.176\)

Round to nearest cent:

\(A_T=63840.18\)
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