Exploration
Building the Formula Yourself
Students fill in a compound interest table year by year, discovering the pattern of repeated multiplication before the formula A = P(1 + r)^t is introduced.
You have $1,000 in an account that earns 6% interest per year. Each year, the interest is added to your balance — so next year, you earn interest on the larger amount. Fill in the table below.
For each row: Interest earned = Starting balance × 0.06. Ending balance = Starting balance + Interest earned. For years 10, 20, and 30, you can skip ahead using a calculator — multiply the previous ending balance by 1.06 repeatedly, or use 1000 × (1.06)t.
Starting amount: $1,000 at 6% per year
| Year | Starting Balance | Interest Earned (6%) | Ending Balance |
|---|---|---|---|
| 1 | $1,000.00 | ||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 | |||
| 10 | (calculate) | ||
| 20 | (calculate) | ||
| 30 | (calculate) |
1.How much interest did you earn in Year 1?
2.How much in Year 10? In Year 20? In Year 30?
3.The interest rate stayed the same at 6%. Why is the dollar amount of interest getting larger each year?
4.Look at the ending balances at Year 10, Year 20, and Year 30. Do they grow by the same amount each decade, or by an increasing amount?
5.Try to predict the ending balance at Year 40 before calculating it.
What pattern do you notice in how each year's balance relates to the previous year's balance?