Compound interest and exponential growth

Last time

Before we start: last time, in Ratio, sharing, maps and best value, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Interest on interest

Put two thousand dollars in a savings account at three percent. After one year you earn interest. After two years, you earn interest on the interest as well. That snowball is compound interest, and it is also how populations grow and cars lose value. Today you calculate it with a single multiplier and one power.

Simple interest

With simple interest, the same amount is added every year. It is a percentage of the original amount only. Two thousand dollars at three percent: each year earns sixty dollars. Over four years, that is two hundred and forty dollars, so the total value is two thousand, two hundred and forty.

Compound interest, year by year

With compound interest, each year's interest is added to the balance, and next year's interest is calculated on the bigger amount. Year one: two thousand times one point zero three is two thousand and sixty. Year two: two thousand and sixty times one point zero three is two thousand, one hundred and twenty-one eighty. You can see it keeps growing by more each year than the sixty dollars of simple interest.

The multiplier method

Doing this year by year is slow. Instead, use the multiplier raised to the number of years. Three percent interest means a multiplier of one point zero three. Four years: one point zero three to the power four. On the calculator that is two thousand, two hundred and fifty-one point zero two dollars. Compare with simple interest, two thousand, two hundred and forty. Compound gives more.