Suppose $10,000 is deposited into a savings account earning 2% interest compounded quarterly. Find the balance in the account 5 years, rounded to the nearest cent.

Answer 1

The formula for the balance in an account with interest compounded quarterly is \[A = P \left(1 + \frac{r}{n}\right)^{nt},\] where $A$ is the final amount (the balance), $P$ is the principal (the initial amount), $r$ is the annual interest rate (expressed as a decimal), $n$ is the number of times per year interest is compounded, and $t$ is the number of years. Substituting, we have \[A = 10000 \left(1 + \frac{0.02}{4}\right)^{4 \cdot 5} = 10000 \left(1 + 0.005\right)^{20} \approx \boxed{\$11,\!048.45}.\]