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Question

What is the balance after 88 years on a deposit of $500\$500, earning 7%7\% interest compounded semiannually?

A.$657.97B.$658.40C.$856.91D.$866.99A. \$657.97 \\ B. \$658.40 \\ C. \$856.91 \\ D. \$866.99

Solution

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Answered 2 years ago
Answered 2 years ago
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In this problem, we have the principal amount pp and the interest rate rr (expressed in decimal) where

p=500, r=0.07p=500, ~r=0.07

However, since the interest is compounded semiannually, it means that the interest is compounded every half of the year, or in other words, twice a year. This means that we divide the interest rate by 22.

r=0.072r=0.035\begin{aligned} r&=\frac{0.07}{2}\\ r&=0.035 \end{aligned}

Also, since the interest is compounded semiannually, the number of interest periods nn is twice a year. Since the period is 88 years,

n=2(8)n=16\begin{aligned} n&=2(8)\\ n&=16 \end{aligned}

Thus, our values are

p=500, r=0.035, n=16p=500, ~r=0.035,~n=16

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