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.
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 interest rate on a perpetuity with the following formula:
Interest Rate = Annual Payment ÷ Perpetuity Price
Thus, we simply substitute in 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%
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 should be on the investment.
The formula for the present value of a perpetuity is a 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
The present value of an annuity formula allows us to check our math when calculating an interest rate on a perpetuity. It also enables us to determine what someone should pay for a perpetuity, given an annual payment and a suitable interest rate or return.
At any rate, our calculated interest rate of 8.33% is correct, since the present value of $60,000 is equal to the present value we were given to use in the first formula.
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