Suppose you put $100 into a savings account today, the account pays 8% compounded semiannually, and you withdraw $50 one year after your initial deposit. What would your ending balance be 20 years after the initial $100 deposit was made, assuming that you make no additional deposits?

A) $250.31
B) $257.45
C) $258.16
D) $430.10
E) $480.10

Question

Cristine Reyes · Accepted Answer

Final Answer : C, Explanation :  First we need to find the balance after one year, when $50 is withdrawn. Using the formula for compound interest compounded semiannually:$A=P\left(1+\frac{r}{n}\right)^{nt}=100\left(1+\frac{0.08}{2}\right)^{2}-50\approx\boxed{129.16}$Now we need to find the balance 20 years later using the same formula:$A=129.16\left(1+\frac{0.08}{2}\right)^{2\cdot20}\approx\boxed{258.16}$which is (C).

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