SmartLearner

When interest on an investment is compounded more frequently than once a year, then the interest rate per time interval will be less than the interest rate for the whole year.

Example:
If interest is compounded quarterly at 2% , then the nominal interest rate is:
2% x 4 = 8% per annum.

The nominal interest rate is also known as the nominal annual interest rate.

1. A bank offers 8% nominal interest compounded monthly.
What is the effective interest rate?

2. Calculate the effective interest rate equivalent to a nominal interest rate of 9,6% compounded quarterly.

3. Calculate the effective interest rate if the nominal rate is :
3.1. 9,2% compounded monthly.
3.2. 8,5% compounded half-yearly.

4. You are quoted a nominal interest rate of 7,2% per annum compounded monthly.
4.1 Calculate the effective rate per annum correct to THREE decimal places.
4.2. If you are quoted an effective rate of 3,4% p.a.
Calculate the nominal rate if calculations are done monthly.

5. Calculate the nominal rate equal to an effective rate of 6,3% p.a if calculations are done quarterly.

1. Sifiso invested R1 200 for 7 years.
How much will it be worth if he is offered interest at 7,8% p.a compounded half-yearly for the first 3 years and 7,2 % p.a compounded monthly for the rest of the period?

2. Makaira invested R 6300 for 11 years.
Calculate how much the investment will be worth if the bank offered interest at 12,4% p.a. compounded monthly for the first 5 years and 9,2% p.a. compounded quarterly for the next 6 years.

3. Thembikihle invests R120 000. She is quoted a nominal interest rate of 7,2% per annum compounded monthly.

3.1. Calculate the effective rate per annum correct to THREE decimal places.
3.2. Use the effective rate to calculate the value of her investment if she invested the money for 3 years.
3.3. Suppose Thembikihle invests her money for a total period of 4 years, but after 18 months makes a withdrawal of R20 000.
How much will she receive at the end of the 4 years?

Financial Mathematics 4