12 FURTHER MATHEMATICS Nominal and effective interest rates

12 FURTHER MATHEMATICS Nominal and effective interest rates

Nominal and effective interest rates Nominal interest rate Compound interest rates are usually quoted as annual rates, or interest rate per annum. This rate is called the nominal interest rate for the investment or loan. Sometimes an annual rate might be quoted, but the interest can be calculated and paid according to a different time period, such as monthly. The time period after which compound interest is calculated and

Nominal and effective interest rates The terms of a compound interest loan or investment are usually quoted as a nominal interest rate followed by a compounding period. The interest rate for the compounding period is easily calculated using simple arithmetic.

Nominal and effective interest rates It must be assumed that there are: � 12 equal months in every year (even though some months have different numbers of days) � 4 quarters in every year (a quarter is equal to 3 months) � 26 fortnights in a year (even though there are slightly more than this) � 52 weeks in a year (even though there are slightly more than this) � 365 days in a year (ignore the existence of leap years). A nominal interest rate is converted to a compounding interest

Nominal and effective interest rates

Nominal and effective interest rates Effective interest rates As a general principle with compound interest, the more frequently interest is calculated and added to your investment or loan (the compounding period), the more rapidly the value of your investment or loan increases. This is illustrated in the next table, which compares the value of a $5000 investment paying a nominal interest rate of 4. 8% per annum with the value of the investment if the interest is calculated on a quarterly or monthly basis, rather than just yearly.

Nominal and effective interest rates

Nominal and effective interest rates As you can see from the table, the more frequently interest is calculated and added, the greater the value of the investment at the end of the year. For this investment, the amounts ranged from $240. 00 when interest is calculated and added annually to $245. 35 when interest is calculated and added monthly. What this means is that an investment where the interest is calculated and added monthly has a higher effective annual interest rate than an investment where interest is calculated and yearly. The effective interest rate is determined as follows.

Nominal and effective interest rates

Nominal and effective interest rates The effective rate for an investment at 4. 8% per annum, compounding quarterly, is 4. 81%. This means that, after 1 year, the interest earned will be 4. 81% of the amount invested. After 1 year, the interest earned by the monthly compounding investment will be 4. 91% of the amount invested. The investment that compounds monthly earns more interest in a year. Instead of writing a table for a whole year in order to calculate the effective interest rates for different loans or investments, we can use the following rule.

Nominal and effective interest rates

Nominal and effective interest rates

Nominal and effective interest rates The amount of interest earned over a particular time period depends on the number of compounds within that time period. In a short time period, the number of compounds has very little effect on the total interest paid or earned; however, over long time periods the number of compounds can have a significant effect on the total interest earned or paid.

Nominal and effective interest rates

WORK TO BE COMPLETED Exercise 8 G – All Questions