The formula for the present value of a future amount
/The formula for the present value of a future amount is used to decide whether to make or receive a payment now or in the future. The calculation shows which option has the higher present value, which drives the decision. The formula for calculating the present value of a future amount, using a simple interest rate, is as follows:
P = A/(1 + nr)
Where:
P = The present value of the amount to be paid in the future
A = The amount to be paid
r = The interest rate
n = The number of years from now when the payment is due
For example, ABC International owes a supplier $10,000, to be paid in five years. The interest rate is 6%. ABC could instead pay the supplier the present value of the amount right now in order to clear the obligation from its accounting records. The calculation using a simple interest rate would be:
P = $10,000 / (1+ (5 x .06)
P = $7,692.31
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The formula for calculating the present value of a future amount using a compounded interest rate, where the interest rate is compounded annually, is:
P = A/(1+r)n
We use the same example, but the interest is now compounded annually. The calculation is:
P = $10,000 / (1+.06)5
P = $7,472.58
The formula for calculating the present value of a future amount using a compounded interest rate, where the interest is compounded multiple times per year, is:
P = A/(1+(r/t))nt
Where:
t = times compounded per year
We use the same example, but the interest rate is now compounded monthly (12 times per year). The calculation is:
P = $10,000 / (1+(.06/12))(5*12)
P = $7,413.72
In short, a more rapid rate of interest compounding results in a lower present value for any future payment.
FAQs
How does the present value formula differ from the future value formula?
The present value formula discounts a future amount back to today by dividing by a compounding factor. The future value formula compounds a present amount forward in time by multiplying by that factor. They are inverse calculations reflecting opposite directions in the time value of money.