Questions: A bank pays interest at the nominal rate of 1.1% per year. What is the effective annual rate if interest is compounded (a) Annually: effective annual rate = % (b) Monthly: effective annual rate = % NOTE: Round all answers to three decimal places.

Solution Steps

To find the effective annual rate (EAR) given a nominal interest rate, we use the formula for compounding interest. For annual compounding, the EAR is the same as the nominal rate. For monthly compounding, we use the formula: \( \text{EAR} = (1 + \frac{r}{n})^n - 1 \), where \( r \) is the nominal rate and \( n \) is the number of compounding periods per year.

For annual compounding, the effective annual rate (EAR) is the same as the nominal rate. Given the nominal rate is \(1.1\%\), the effective annual rate is also \(1.1\%\).

To find the EAR for monthly compounding, we use the formula: \[ \text{EAR} = \left(1 + \frac{r}{n}\right)^n - 1 \] where \(r = 0.011\) (the nominal rate as a decimal) and \(n = 12\) (the number of compounding periods per year).

Substituting the values, we get: \[ \text{EAR} = \left(1 + \frac{0.011}{12}\right)^{12} - 1 \]

Calculating this gives: \[ \text{EAR} \approx 0.01106 \]

Converting this to a percentage: \[ \text{EAR} \approx 1.106\% \]

Final Answer