Present Value: What if I could get tomorrow’s money today?

Present value is the opposite of future value but can be calculated using the same formula.

Instead of asking what value present-day money will have in the future, the calculation for present value asks what value future money will have today (if it were paid today). When calculating the present value of an amount due in the future, it is fair to assume that the amount paid today will be something less than the amount paid in the future. If an obligation will equal a certain amount in three years, it can be discounted to some lesser amount today.

Assume that you are entitled to be paid $1,000 in three years by a business associate. How much should your business associate pay you today to discharge his debt that will be due in three years. Assume the interest rate is 4% compounded annually.

The question can be framed like this:  What is the present value of $1,000 to be paid in three years based on a 4% interest rate (or discount rate) compounded annually?

The formula is:  FV = PV (1 + i)ⁿ

where FV is future value, PV is present value, “i” equals interest rate, and “n” equals the payment period (in years).

While the present value formula is the same as the future value formula, the FV figure is known to us this time, and the PV figure is missing. As we complete the formula it will be necessary to apply some simple algebra to determine the PV.

FV = PV (1 + i)ⁿ

$1,000 = PV (1 + .04)³

$1,000 = PV (1.124864)

[Algebra: We now need to isolate PV on one side of the equation.
To do this, divide both sides by 1.124864]

$1,000/1.124864 = PV

Present Value equals $1,000 divided by 1.124864.

Therefore, PV = $888.99.

So, the present value of $1,000 to be paid in three years (at 4% interest) is $888.99. If this were a business transaction, a loan repayment or an out-of-court settlement of a legal dispute, a payment of $888.99 today would effectively satisfy the obligation to pay $1,000 in three years.

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