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Other Fields Homework Help Finance Topic started by: Catracho on Oct 14, 2018



Title: Find the interest rate needed for the sinking fund to reach the required amount. Assume that the com
Post by: Catracho on Oct 14, 2018
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.)​


Title: Re: Find the interest rate needed for the sinking fund to reach the required amount. Assume that the
Post by: bio_man on Oct 14, 2018
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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