# Effective Interest Rates

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Nominal vs. Effective interest rates

The most common question from chapter 2 is when to divide annual rate by the number of compounding periods and when to use the effective rate conversion formula to calculate effective interest rates for compounding periods < 1yr. Remember that you must discount future cash flows with EFFECTIVE interest rate for the interest paying (or compounding) periods. All interest rates are quoted per annum and specify compounding (or interest paying) periods (or frequency). This is NOMINAL interest rate.

1. Nominal annual interest rate: Nominal interest rate is simply a proportion of the principal that is paid as interest irrespective of how (in one payment or in instalments) or when it is paid (whether it is paid at the beginning, during or end of the period). Time value of money (i.e. compounding) is not considered in this case. It is NOT a rate , simply means that the total amount of interest payment of return! Nominal rate of 10% p.a ( . is 10% of face value per annum. This is similar to a coupon rate on a bond. Where n = nominal, m = number of compounding periods per annum. Example 1: ANZ is paying 10% pa interest on a one your term deposit with interest payable A. at maturity (nominal interest rate, pa = B. Half yearly (nominal interest rate, pa = C. Quarterly (nominal interest rate, pa = D. Monthly (nominal interest rate, pa = E. daily (nominal interest rate, pa =

. , . , . , . , . ,

Irrespective of the interest paying frequency, the total interest payment is 10% of principal. For example, for the principal of \$100, total interest payment is 0.1 x \$100 = \$10, which is paid in one payment at the end of period if compounding is once a year, two \$5 payments at the end of two 6 month periods, four \$2.5 payments at the end of each quarter, etc. In each case the total sum of interest payment ignoring time value (or compounding) is \$10. So, nominal interest of 10% pa compounding monthly = nominal interest rate of 10% compounding ,...

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