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Express Lane Plus
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8 months ago
Find the amount of each payment to be made into a sinking fund which earns 7% compounded quarterly and produces $34,000 at the end of 3.5 years. Payments are made at the end of each period.
The payment size is $?                                                                                                 ​(Do not round until the final answer. Then round to the nearest​ cent.)
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Educator
8 months ago
Here you'll need the annuity formula:

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

A = future value amount \(\rightarrow\) 34 000
R = regular deposit/payment
r = interest rate \(\rightarrow\) 7% or 0.07
n = compounding periods per year \(\rightarrow\) 4
t = total number of deposits \(\rightarrow\) 4 + 4 + 4 + 2 = 14

\(34000=\frac{R\left[\left(1+\frac{0.07}{4}\right)^{14}−1\right]}{\frac{0.07}{4}}\)

\(34000\left(\frac{0.07}{4}\right)=R\left[\left(1+\frac{0.07}{4}\right)^{14}−1\right]\)

\(\frac{34000\left(\frac{0.07}{4}\right)}{\left[\left(1+\frac{0.07}{4}\right)^{14}−1\right]}=R\)

\(R=2164.291\)

Rounded: R = 2164.29

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