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Question

# What is the balance after $8$ years on a deposit of $\500$, earning $7\%$ interest compounded semiannually?$A. \657.97 \\ B. \658.40 \\ C. \856.91 \\ D. \866.99$

Solution

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In this problem, we have the principal amount $p$ and the interest rate $r$ (expressed in decimal) where

$p=500, ~r=0.07$

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 $2$.

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

Also, since the interest is compounded semiannually, the number of interest periods $n$ is twice a year. Since the period is $8$ years,

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

Thus, our values are

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

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