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Lesson 3, Topic 5
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# Annuity

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This is a series of equal sum of money paid at regular intervals. It is usually paid annually at the end of a year.

We can calculate annuity using the formula of a geometric sequence.

Total amount = $$\frac{P \left [ \left ( 1 + \frac{r}{100} \right)^n \; – \; 1 \right] }{\left ( 1 + \frac{r}{100} \right) \; – \; 1 }$$

Example: Find the amount of an annuity of #10,000 paid yearly for 3years at 8% per annum.

Total amount = $$\frac{10,000 \left [ \left ( 1 + \frac{8}{100} \right)^3 \; – \; 1 \right] }{\left ( 1 + \frac{8}{100} \right) \; – \; 1 }$$

= $$\frac{10000(1.08)^3 – 1}{1.08 \; – \; 1}$$

= #32464.00

Exercise.

1. Find the amount credited by an annuity of #60000 payable yearly for 4 years at 4% interest.

2. Find the amount arising from an annuity of #24000.00 per annum payable yearly for 9years, with compound interest at 5% per annum.

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