How to Calculate Monthly Returns on Perpetuities

How to Calculate Monthly Returns on Perpetuities
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A perpetuity refers to a series of payments that has no foreseeable end. It keeps paying a certain amount of money regularly into perpetuity. You may encounter a perpetuity when a project generates a certain amount of profit or when you buy a stock that pays you dividends regularly. There are three types of perpetuities: regular perpetuities, perpetuities due and growing perpetuities. Each type requires you to use a different formula to calculate the monthly returns.

Regular Perpetuity

Determine the present value of the perpetuity. This is the amount of money you pay today to get returns every month, starting from next month's return into perpetuity. For example, this may be the initial investment on a project or the price of a dividend-paying stock.

Find the interest rate on the perpetuity. If the interest rate is expressed as an annual figure, divide it by 12 to get the monthly interest rate. For example, if you have an interest rate of 6 percent per year, then your monthly interest rate is 0.5 percent per year.

Divide the present value of the perpetuity by the monthly interest rate to get the amount of money you get each month. For example, if you put in an investment of $100,000 and get monthly returns at 0.5 percent per month, then you get $500 each month, starting from the next month.

Perpetuity Due

Calculate the present value of the annuity due. With an annuity due, you get the monthly payments starting from the same day as your initial investment. Compared to a regular annuity, therefore, you have one extra payment from an annuity due.

Divide the annual interest rate by 12 to get the monthly interest rate, if necessary.

Insert the present value, as represented by "PV," and interest rate, as represented by "r," into the following formula: (PV * r) / (1 + r). For example, with a present value of $100,000 and interest rate of 0.5 percent per month, your monthly returns will be $497.51, derived from ($100,000 * 0.005) / (1 + 0.005).

Growing Perpetuity

Find out the perpetuity's present value, monthly interest rate and monthly growth rate. The monthly returns on a growing perpetuity increase according to a constant rate of growth, with the initial returns being the lowest. Divide the annual growth rate by 12 to get the monthly growth rate, if necessary.

Deduct the monthly growth rate from the monthly interest rate. For example, if the monthly interest rate is 0.5 percent and the monthly growth rate is 0.25 percent, you have 0.25 percent.

Multiply the result from Step 2 by the present value of the perpetuity to get the amount of the first monthly payment. For example, if your present value is $100,000, your first monthly payment is $250.

Multiply the initial payment by (1 + r ) ^ (t - 1) to get the monthly payment at any point in time. In this formula, "r" represents the interest rate and "t" stands for the number of payments. For example, if you want to obtain the amount you'll get at the 11th payment, perform the following calculation: $250 ((1 + 0.0025) ^ (11 - 1)) = $256.32.