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Express Lane Plus
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4 months ago
Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period.

$30,000 to be accumulated in 10  ​years; annual payments of payments of $2458

The interest rate needed is approximately?  %
(Round to two decimal places as​ needed.)​
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Educator
4 months ago
F = final \(\rightarrow\) 30 000
P = principal \(\rightarrow\) 2 458
t = years \(\rightarrow\) 10
n = compounding periods per year \(\rightarrow\) 1 (annual)
r = interest rate

Compound interest formula: \(F=P\left(1+\frac{r}{n}\right)^{nt}\)

\(30000=2458\left(1+r\right)^{10}\)

\(\frac{30000}{2458}=\left(1+r\right)^{10}\)

\(\sqrt[10]{\frac{30000}{2458}}=1+r\)

\(\sqrt[10]{\frac{30000}{2458}}-1=r\)

\(r=0.2842\)

\(\therefore r=28.4\%\)

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