Financial calculators may look intimidating, but they are particularly helpful with questions that involve streams of cash flow over a certain period of time. This is the case with perpetuities. A perpetuity is a cash flow that continues indefinitely (into perpetuity). A growing perpetuity refers to a growing stream of payments. The hardest part about calculating this number on a financial calculator is determining "r," or the rate to discount rate.

- Skill level:
- Easy

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## Instructions

- 1
Review the formula for a perpetuity. The formula is: C / r, where "C" equals cash flows paid at the end of each year at "r," which is the rate of interest. A growing perpetuity assumes the cash flows are growing at a certain rate every year. The formula for growing perpetuity is: C / ( r - g ), where "g" is the growth rate of cash flows.

- 2
Look for the IRR (internal rate of return) calculation on your calculator. If you do not see the key marked, you need to look up the key for IRR in your manual.

- 3
Put your calculator in finance mode.

- 4
Define your variables. Let's assume you have a growing annuity problem to do (this is a common growing perpetuity problem). Your annuity pays at the end of year 1, and the payments grow at a rate of 6 per cent per year. The current interest (discount) rate is 8 per cent. £65 is PMT (payment), and r = (1 + discount rate)/(1 + growth rate) - 1 or 1.08 / 1.06 - 1. The rate is .0189.

- 5
Input these variables into the IRR formula for your calculator. £65 is PMT, or the regular cash flows, and "r" is the rate at which the perpetuity will grow considering a growth rate. Hit "Enter" to calculate.