Compound Interest Lab: Compare Growth Over Time
Change principal, rate, years, and compounding frequency. Compare compound and simple interest, effective rates, and doubling times.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 8 minutes.
How does it work?
- Set a starting balance, a nominal annual rate, and a whole number of years.
- Choose how often interest is credited, or open a preset.
- Read the year-end chart and table, then try the challenges.
What will you get?
Compare growth paths and distinguish a nominal rate from an effective annual rate.
What does the model assume?
- These balances are hypothetical calculations, not quoted returns or forecasts.
- The nominal annual rate stays fixed. There are no later deposits or withdrawals, taxes, or fees.
- Interest is credited at the end of each compounding period and then earns interest. Daily compounding uses 365 equal periods per year.
- Balances are calculated without rounding individual interest credits. Currency outputs are rounded for display.
- The chart connects year-end balances; it does not show the steps between interest-credit dates.
- The logarithmic doubling time solves the growth equation using fractional periods. First credited doubling rounds that time up to an interest-credit date.
- At 0%, interest is zero and a positive starting balance never doubles.
Which setup would you like to try?
What can you change?
Range: 100 to 10000 dollars.
Range: 0 to 20 %.
Range: 1 to 40 years.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Compound balance | 1,628.89 | dollars |
| Compound interest earned | 628.89 | dollars |
| Simple-interest balance | 1,500.00 | dollars |
| Effective annual rate | 5.0000 | % |
| Doubling time from the growth equation | 14.2067 | years |
| First credited doubling | 15.0000 | years |
- Compound interest: solid line
- Simple interest: dashed line
Read the year-end balances
| Year | Compound interest: solid line | Simple interest: dashed line |
|---|---|---|
| 0 | 1,000.00 | 1,000.00 |
| 1 | 1,050.00 | 1,050.00 |
| 2 | 1,102.50 | 1,100.00 |
| 3 | 1,157.63 | 1,150.00 |
| 4 | 1,215.51 | 1,200.00 |
| 5 | 1,276.28 | 1,250.00 |
| 6 | 1,340.10 | 1,300.00 |
| 7 | 1,407.10 | 1,350.00 |
| 8 | 1,477.46 | 1,400.00 |
| 9 | 1,551.33 | 1,450.00 |
| 10 | 1,628.89 | 1,500.00 |
Can you reach these targets?
Start with $1000 and use annual compounding for two years. Find a rate that gives a $1210 balance.
- Target: Starting principal = 1000 dollars; tolerance 0 dollars.
- Target: Time invested = 2 years; tolerance 0 years.
- Target: Compound balance = 1210 dollars; tolerance 0.01 dollars.
- Interest-credit schedule (Annually)
Use $1000 at a nominal 12% for one year. Choose monthly compounding and compare the two balances.
- Target: Starting principal = 1000 dollars; tolerance 0 dollars.
- Target: Nominal annual rate = 12 %; tolerance 0 %.
- Target: Time invested = 1 years; tolerance 0 years.
- Target: Compound balance = 1126.83 dollars; tolerance 0.01 dollars.
- Target: Simple-interest balance = 1120 dollars; tolerance 0.01 dollars.
- Interest-credit schedule (Monthly)