Financial Math: Present Value

Calculate Present Value

Definition

The present value of money is, simply put, how much a future amount is worth now. Suppose you have been promised a payment of $1,000 in 10 years. That money has a present value much less than $1,000 because it will grow to $1000 over those 10 years.

Present Value Formula

$$ \huge P = \frac{F}{(1+r)^t} $$

The present value of money is equal to the future value divided by the interest rate plus 1 raised to the t power, where t is the number of months, years, etc. Make sure to use the same units of time for both the interest rate and the time.

Examples

Here's an example to make it more clear: Bob wants to save $20,000 to buy a new car in 4 years without obtaining a loan. He knows he can invest the money in a Certificate of Deposit earning 6% annually. To find out how much he needs today in order for it to grow to $20,000, he uses the present value formula:

$$ \huge P = \frac{F}{(1+.06)^4} = $15,841.90 $$

If he saves that much money today at 6% interest, it will grow to the $20,000 in 4 years.

Or, what about Jane, who wins a $1 Million contest at a national restaurant chain. Because that money will be paid out in $50,000 checks each year for 20 years, she wonders how much that last $50,000 check will really be worth when adjusted for inflation. She too can use the present value formula to determine what that payment will be worth in terms of today's dollars. After all, $50,000 twenty years from now certainly won't be worth as much as it is today. She's going to assume a long term inflation rate of 3% over that span.

$$ \huge P = \frac{$50,000}{1.03^{19}} = $28,514.30 $$

Note that I used 19 for t, because that 20th payment is only 19 years from now, assuming she gets the first payment right away. Even though it will be a check for $50,000, that will only be worth the equivalent of $28,514.30 in today's dollars because it will have been devalued by inflation (estimated at 3% for this problem).

See more related lessons on our Financial Math page

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