Math 1 · Unit 8 · Lesson 2 · part 2 of 5
Interest on interest
Lesson 1 was the line: simple interest pays on the principal only, so it adds the same dollars every year.
Interest on interest
Lesson 1 was the line: simple interest pays on the principal only, so it adds the same dollars every year. Compound interest pays on the principal and on the interest already earned. Each year's interest is added to the account, and next year it earns interest too. When that happens once a year, the account is compounded annually.
Same $1,000 at 5%.
| year | interest earned this year | balance |
|---|---|---|
| 0 | $1,000.00 | |
| 1 | 5% of 1,000.00 = $50.00 | $1,050.00 |
| 2 | 5% of 1,050.00 = $52.50 | $1,102.50 |
| 3 | 5% of 1,102.50 = $55.13 | $1,157.63 |
| 4 | 5% of 1,157.63 = $57.88 | $1,215.51 |
Look at the middle column: $50.00, then $52.50, then $55.13, then $57.88. The dollars added each year are growing. In Unit 3 words, the average rate of change (the change in the balance over each one-year interval) gets bigger every year. A line has the same rate of change everywhere, so this is not a line.
Build the two accounts side by side, one year at a time, and watch the compound column pull ahead.