What is the formula for the present value of a future amount?

The formula for calculating the present value of a future amount using a simple interest rate is:

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 amoount 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

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.

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