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HSC Standard Maths Resources

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13.2 Compound Interest

Simple interest earns interest only on the principal amount of investment, compound interest earns interest not just only on the principal but also on the interest previously earned. The basic formula to remember is shown: At a basic level, you can be given three out of the four things in the formula and can be asked to calculate that fourth one. So, for example, FV, i and t are given and you need to calculate PV.

Like simple interest, whenever answering these questions make sure i and t have consistent compounding periods. If not, then make them consistent.

Some possible variations:

• Instead of asking for PV or FV, question can also ask you to calculate interest earned in a given year in which case it would be a slight variation of formula.
• Instead of having a constant interest rate, rate can be different in different time periods.
• Inflation, which is the increase in price of goods and services, operates the same way as compound interest rate in terms of calculations.

Example 1

What is the future value of an investment of \$10,000 if it earns 7% p.a. compounded quarterly for 3 years?

Example 2

What is the amount of interest earned in third year for an investment of \$15,000 today if it earns 3.5% p.a. compounded annually for 6 years?

Example 3

What is the future value of an investment of \$30,000 in 3 years if it earns 2.89% p.a. compounded annually in year 1, 2.75% p.a. compounded quarterly in year 2 and 3.1% p.a. compounded annually in year 3?

Example 4

Inflation rate in a country is 2.5% p.a. What is the expected price of an apartment in 3 years if its current price is \$350,000?