Perpetuities

Perpetuities are annuities where a sum of money is permanently invested which provides regular payments that continue indefinitely.

The Formula

You will be asked to find the regular payment ( $Q$ ), the principal ( $P$ ) and the interest rate ( $r$ ).

$Q=\dfrac {Pr}{100}$
$P=\dfrac {100Q}r$
$r=\dfrac {100Q}P$

These formulas can be used for both simple and compounding interest rates and will only work if $Q$ and $r$ are in the same time unit.

Example 1

A wealthy business leader wishes to provide a scholarship to assist disadvantaged students attend secondary school. To cover the fees, the scholarship would need to provide $1,500 per term. They decide to invest with an institution that offers an interest rate of 7% p.a. How much would the business leader to need invest?

We are told the values of $Q$ and $r$ .

$Q=1,500$ per term
$r=12%$ p.a. $=3%$ per term

Use the perpetuity formula to find $P$ .

$P=\dfrac {100\times 1,500}3$
$P=50,000$

The principal required to provide $1,500 per term at a rate of 7% per annum is $50,000.

Use of Calculator

The TVM solver on your calculator can calculate the answer to most questions. Make sure to check the amount of marks a question is worth and show the appropriate working.

Use the formula (not the TVM solver) if the principal is unknown.

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