Find the nominal rate , compounded monthly that is equivalent to
a) 5 1/4 % effective
To find the nominal rate compounded monthly that is equivalent to 5 1/4% effective, we need to first convert the effective rate to a decimal.
5 1/4% is equal to 5.25%, or 0.0525 as a decimal.
Next, we can use the formula for converting an effective interest rate to a nominal interest rate compounded m times per year:
Nominal Rate = [(1 + Effective Rate/m)^m - 1] * 100
In this case, we want to compound monthly, so m = 12.
Nominal Rate = [(1 + 0.0525/12)^12 - 1] * 100
Nominal Rate = [(1 + 0.004375)^12 - 1] * 100
Nominal Rate = [1.004375^12 - 1] * 100
Nominal Rate = [1.056611719 - 1] * 100
Nominal Rate = 0.056611719 * 100
Nominal Rate = 5.6611719
Therefore, the nominal rate compounded monthly that is equivalent to 5 1/4% effective is approximately 5.661%.