## Tuesday, June 30, 2009

### PRESENT VALUE

Present Value

The present value of money is how much a future amount is worth now. Suppose you want to have \$1000 in 10 years. That money has a present value that is much less that \$1000 because it will grow to \$1000 over those 10 years.

P = 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.
NOTE: the above formula is meant for annual compounding. It should be adjusted to reflect monthly or even weekly or daily compounding.
For monthly compounding, r needs to be divided by 12 and t times 12.
For weekly compounding, r needs to be divided by 52 and t times 52.
For daily compounding, r needs to be divided by 360 and t times 360 (US standard).
For other period, one needs to adjust the r and t accordingly to reflect the true amount needed.

Here's an example to make it more clear: Bob wants to save \$20,000 to buy a new car in 4 years. 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:

P = 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. 