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Find the interest rate needed for the sinking fund to reach the required amount. Assume that the com
Catracho
Catracho
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Find the interest rate needed for the sinking fund to reach the required amount. Assume that the com
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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bio_man
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8 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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