How to Calculate PV From PMT

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You can determine the value in today's dollars of a stream of future, periodic payments using the present value of an annuity equation. An annuity is an amount of money paid at regular intervals for a certain period of time. An annuity can be in several forms, such as a contract in which an investor receives payments from an insurance company or a loan with fixed payments. The present value of an annuity equation calculates the present value, or PV, of an annuity based on the payment, or PMT, and other factors. Present value is what the future payment stream is worth based on the terms in the equation.

Things You'll Need

  • Calculator
  • Input the payment, interest rate and number of periods of an annuity into the present value of an annuity equation "PV = PMT[(1 - (1 / (1+ i)^n)) / i]." In the equation, "PV" equals the present value, "PMT" equals the constant payment received at the end of each period, "i" equals the interest rate per period and "n" equals the number of periods. In the following example, use a $1,000 annual payment, a 5 percent annual interest rate and a 10-year period. This yields the equation "PV = $1,000[(1 - (1 / (1 + 0.05)^10)) / 0.05]."

  • Add the numbers inside the parentheses that contain the exponent. In the example, add 1 plus 0.05. This equals 1.05, which leaves "PV = $1,000[(1 - (1 / (1.05)^10)) / 0.05]."

  • Raise the number inside the parentheses to the power of the exponent. In the example, raise 1.05 to the power of 10, which equals 1.6289. This leaves "PV = $1,000[(1 - (1 / 1.6289)) / 0.05]."

  • Divide the numerator by the denominator of the fraction inside the parentheses. In the example, divide 1 by 1.6289, which equals 0.6139. This leaves "PV = $1,000[(1 - 0.6139) / 0.05]."

  • Subtract the result from 1 inside the parentheses. In the example, subtract 0.6139 from 1, which equals 0.3861. This leaves "PV = $1,000(0.3861 / 0.05)."

  • Divide the numerator by the denominator of the fraction inside the parentheses. In the example, divide 0.3861 by 0.05, which equals 7.722. This leaves "PV = $1,000(7.722)."

  • Multiply the remaining numbers. In the example, multiply $1,000 by 7.722, which equals $7,722. This is the present value of a 10-year annuity that makes equal, annual payments of $1,000 with a 5 percent annual interest rate.

Tips & Warnings

  • This equation applies only to annuities with constant payments made at the end of each period.

References

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