Answer
a) $4.20\%$
b) $4.28\%$
c) $4.29\%$
Work Step by Step
To find the Effective Annual Rate (EAR) from a nominal annual interest rate of $4.2\%$, we use different formulas depending on the compounding method.
a) Interest is compounded annually.
When compounded annually, the EAR is the same as the nominal rate:
$$EAR=4.20\%.$$
b) Interest is compounded monthly.
Use the formula:
$$
EAR=\left(1+\frac{r}{n}\right)^{n}-1 =\left(1+\frac{0.042}{12}\right)^{12}-1\approx 0.0428=4.28\%$$
c) Interest is compounded continuously.
Use the formula:
$$EAR=e^r-1=e^{0.042}-1\approx 4.29\%$$
