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

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.

See also

Simple Interest
Compound Interest
Annuity Investments