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Find the interest rate needed for the sinking fund to reach the required amount. Assume that the com
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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. $40,000 to be accumulated in 9 years; annual payments of $3507
The interest rate needed is approximately
%.?
(Round to two decimal places as needed.)
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2 months ago
We use the sinking fund payment formula to find the interest rate i - we assume it's compounded annually, hence \(n\) is 9.
\(R=\frac{Si}{\left(1+i\right)^n-1}\)
\(3507=\frac{\left(40000\right)i}{\left(1+i\right)^9-1}\)
Multiply both sides by the denominator:
\(3507\left[\left(1+i\right)^9-1\right]=\left(40000\right)i\)
Expand the left side:
\(3507\left(1+i\right)^9-3507=\left(40000\right)i\)
Moving everything over to the left side and set it equal to y.
\(3507\left(1+i\right)^9-40000i-3507=y\)
Now graph it: (shown below)
You should get 0.05819 as a root. Multiply this by 100% to get:
5.82
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