How to Calculate the Interest Rates on Perpetuity

By Motley Fool Staff – Oct 4, 2025 at 10:14PM

Key Points

Perpetuities pay a fixed annual sum; interest rate calculated by dividing payment by price.
Example: $5,000 annual perpetuity for $60,000 has an 8.33% interest rate.
Validate investment value using Present Value formula, confirming fair price.
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In 1648, a Dutch government authority issued a bond that promised to pay interest forever. Written on goatskin, five such bonds are known to exist today. Yale University owns one, and in 2015, collected 12 years' worth of back interest, which amounted to all of $153.

This bond is the perfect example of a perpetuity -- a promise to pay out a certain amount on a regular basis, forever. Let's take a look at how we can calculate an interest rate for a perpetuity, using an example.

Image source: Getty Images.

The formula

How to calculate the interest rate on a perpetuity

Suppose that you have the opportunity to buy a perpetuity for $60,000 that promises to pay you $5,000 every year, but you want to calculate what your rate of return (interest rate) will be.

We can calculate the interest rate on a perpetuity with the following formula:

Interest Rate = Annual Payment ÷ Perpetuity Price

Thus, we simply substitute our two variables into the formula to get the following:

Interest Rate = $5,000 ÷ $60,000

The next step is to do the division:

Interest Rate = 0.0833

Finally, we multiply the rate by 100 to convert it into percentage terms:

Interest Rate = 8.33%

Check your work

We can use another formula to check our work. This is called the present value of a perpetuity formula. It tells us how much a perpetuity should be worth, provided that we know how much it will pay each year and what the interest rate on the investment should be.

The formula for the present value of a perpetuity is as follows:

Present Value = Annual Payment ÷ Interest Rate

We'll plug in the interest rate we calculated above (8.3%) and the annual payment we will receive ($5,000) into the formula.

Present Value = $5,000 ÷ 0.0833

Next, we divide to find out what a perpetual stream of $5,000 payments should be worth at an 8.33% interest rate.

Present Value = $60,000