Compound Interest

      Compound interest is just a little more complex. With compound interest, instead of multiplying by the amount you originally put into the bank, you multiply by what you have now.
      So, let's say I invest $1000, again at 8% interest. After one year, I have $1000 + 0.08 * $1000, or $1080. Notice that this is the same as 1.08 * $1000. You have taken P (the amount you invested) and multiplied it by (1+r), where r is the interest rate. After two years, I will now have 1.08 * $1080, or $1166.40. Here we used what we had after last year for our "P-value", not what we originally invested. After three years, we will multiply this new number by 1.08, so we have

Each year we are taking what we have, and multiplying it by (1 + r). We can used exponents to simplify this - when we multiply something by (1 + r) a certain number of times, let's say n, we can write that as

Now we can write down a formula for the total amount of money we have after n years, assuming we started out with P and the interest rate is r.

What does this tell us? It means: take what you started with. Multiply it by (1+r) repeatedly (a total of n times). The result is your amount.

See how simple all this is? If you're not a "math person" these formulas might look intimidating at first. Don't let them! They turn out to be pretty simple ideas, it's just the way they're written that makes them look difficult. Just take your time, read through them step by step, and try to tell yourself in words what the formula says. Before long you'll feel confident reading formulas.

Go on to the annuities section