How you work with an interest rate depends on what type of interest rate you are given, and what you want to do with it. An exam question shouldn't refer to 'an interest rate of 10% per annum' as it's not specific enough.If you have an interest rate of i = 10% per annum effective, then if you want the nominal interest rate convertible monthly, i(12), you use the formula i(12) = 12[(1+i)^(1/12) - 1]. You would need i(12) if you were calculating a(12):<10>, for example, as i(12) appears in the denominator of this annuity factor.
If you have an interest rate of i = 10% per annum effective, then if you want the monthly effective interest rate, you use the formula (1+i)^(1/12) - 1. This is the same as i(12)/12. You would need the monthly effective interest rate if you were creating a loan schedule for a loan that was repaid by monthly repayments, in arrears, for example.
If you have a nominal interest rate of 10% per annum convertible monthly, so i(12) = 10%, then you can calculate the effective monthly interest rate as i(12)/12.
If you have a nominal interest rate of 10% per annum convertible monthly, so i(12) = 10%, then you can calculate the effective annual interest rate using i = (1 + i(12)/12)^12 - 1. This formula is a rearrangement of the general formula i(p) = p[(1+i)^(1/p) - 1]. You would need the effective annual interest rate if you were calculating a present or accumulated value, working in years.
