Question

In: Finance

effective annual interest rate

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?

Solutions

Expert Solution

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%

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