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

Quizplus · Accepted Answer

First we need to find the balance after one year, when $50 is withdrawn.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).

Suppose You Put $100 into a Savings Account Today, the Account