Question

Identify the following interest rate statements as either nominal or effective: (a) 1.3% per month; (b) 1% per week compounded weekly; (c) 15% per year compounded monthly; (d) effective 1.5% per month compounded daily; (e) 15% per year compounded semiannually; (f) 3% per quarter; (g) 3% per quarter compounded continuously.

Answer 1

Before we identify the following interest rates, we must be clear about what is the nominal and effective rate of interest.

The Nominal rate of interest is what is quoted without taking compounding into account. That is a 10% compounded or 5% compounded monthly both are nominal, as they don't take into account the compounding effect. It is only the claimed or quoted interest rate and doesn't give the same yield.

While the Effective rate of interest is the actual interest rate that is applied and which takes the compounding into account. The interest rate claimed to be 5% per year compounded monthly wouldn't be effective, As the actual interest rate applied per annum would differ from the quoted. That is a bank claiming 5% per year compounded monthly and another 5% per year compounded yearly are different. To find out which one gives is a higher return, we need to find the effective interest rate. Overall it is the interest rate that gives the same yield as quoted.

Therefore,

(a) 1.3% per month: It is an effective rate of interest.

As the quoted and actually applied interest rate would be the same as 1.3% per month.

b) 1% per week compounded weekly: It is an effective rate of interest.

As the actual interest rate would be the same as quoted. It is not delusionary, and a bank or person claiming to give 1% per week compounded weekly would result in the same yield as quoted.

(c) 15% per year compounded monthly; It is a nominal interest rate.

As the quoted interest rate is 15% per year compounded monthly, we don't know what the actual interest rate applied will be. And it only the quoted interest rate.

(d) Effective 1.5% per month compounded daily. It is an effective rate of interest

As it is said to be the effective 1.5% or month compounded daily, it means that the compounding effect has been taken into account, and then it is quoted to be 1.5% per month compounded daily.

(e) 15% per year compounded semiannually; It is a nominal rate of interest.

As the real return would differ from the quoted, It will compound semianuually per year. The interest rate applied would differ from 15%. Therefore it is only the quoted rate of interest and nominal.

(f) 3% per quarter: It is an effective rate of interest.

As the real return would be the same, and it wouldn't differ even after taking into account the compounding effect. Therefore it is the actual rate of interest or the effective.

(g) 3% per quarter compounded continuously. It is a nominal rate of interest.

As the actual return on it will differ, and the compounding effect has not been taken into account. Therefore it is only quoted or nominal rate of interest. It will compound continuously in the quarter, and at the end of the period, the interest rate applied wouldn't be 3%.