Interest Rates

When you invest money, you expect to earn a certain rate of interest on your money. Likewise, when you borrow money, the person who lends you money expects to earn interest on that loan.

Let's say you borrow $100 from a friend for one year and promise to pay 10% interest at the end of that time, in addition to repaying the principal. The amount of interest you will owe is $10 (10% * $100 = $10), so you have to pay your friend $110 at the end of the year. The amount you get at the beginning of the period, $100, is referred to as the present value (PV) and the amount you pay in the future, $110, is referred to as the future value (FV). The formula for one interest period is:

PV * (1 + r) = FV

If you were to borrow the money for three years and interest is charged at the end of each year, you could calculate how much you have to repay by adding on interest at the end of each time period:

(($100 * (1 + 10%)) * (1 + 10%)) * (1 + 10%)
= $100 * (1 + 10%)3
= $133.10

When interest accumulates on interest over successive periods, this is referred to as compounding. The general formula for calculating future value in this situation is as follows:

PV * (1 + r)n = FV,
  r = interest rate per period
  n = number of periods

Typically, we will want to find the present value of a future payment. Using a bit of algebra on the above equation, we get the following formula:

PV =    FV   
(1 + r)n