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Express Lane Plus
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8 months ago
 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$2458The interest rate needed is approximately?  %(Round to two decimal places as​ needed.)​ Read 72 times 1 Reply
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Educator
8 months ago
 F = final $$\rightarrow$$ 30 000P = principal $$\rightarrow$$ 2 458t = years $$\rightarrow$$ 10n = compounding periods per year $$\rightarrow$$ 1 (annual)r = interest rateCompound 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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