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Express Lane Plus
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5 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. $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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Educator
5 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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