Question

You have received a loan from a bank with a quoted rate of 18 percent compounded monthly. What is the Effective annual interest rate of the loan?

Answer 1

The effective annual rate is calculated when the interest is compounded more than once a year.

HIgher compound rate will provide a higher effective annual rate.

Rate of interest (r) = 18%

Number of compounding periods (n) = 12

\( \begin{align*}\rm\text{Effective annual interest rate} &= \left ( 1+\frac{r}{n} \right )^{n}-1\\ &=\left ( 1+\frac{0.18}{12} \right )^{12}-1\\ &= \left ( 1.015 \right )^{12}-1\\ &= 0.1956 \rm\text{ or } 19.56\%\end{align*} \)

Hence, the effective annual rate of the loan is 19.56%

The effective annual rate of the loan is 19.56%