Interest Rate Lab: Compare Nominal and Real Balances
Set a principal, nominal rate, compounding, and inflation. Compare balance growth with purchasing power and the exact real annual rate.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 8 minutes.
How does it work?
- Change a control to update the table and diagram.
- Open a preset to compare settings, then try the challenges.
What will you get?
Compare the model’s outputs, explore its presets, and check two challenges.
What does the model assume?
- The nominal annual rate and annual inflation rate stay fixed. No deposits, withdrawals, fees, or taxes apply.
- Interest stays invested and is credited at each period’s end. Daily compounding uses 365 periods per year.
- APY is (1 + r/n)ⁿ − 1. The exact real annual rate is (1 + APY)/(1 + inflation) − 1, using decimal rates.
- The approximation subtracts annual inflation from APY, not from a nominal rate with a different compounding basis.
- Today’s purchasing power is the nominal balance divided by (1 + inflation) raised to the number of years. The values are illustrative, not a forecast or financial recommendation.
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.
Range: -5 to 25 %.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Nominal balance | 1,790.85 | dollars |
| Interest earned | 790.85 | dollars |
| Annual percentage yield | 6.00 | % |
| Exact real annual rate | 3.92 | % |
| Approximate real annual rate | 4.00 | % |
| Balance in today’s purchasing power | 1,469.12 | dollars |
Solid line: nominal balance. Dashed line: balance in today’s purchasing power.
After 10 years, the nominal balance is 1,790.85 dollars and its purchasing power is 1,469.12 dollars at the starting price level.
Can you reach these targets?
Use annual compounding and 4% inflation. Find the nominal rate that holds purchasing power constant.
- Target: Annual inflation = 4 %; tolerance 0 %.
- Target: Exact real annual rate = 0 %; tolerance 0.001 %.
- Compounding frequency (Annually)
Set $1000, a 12% nominal annual rate, one year, and zero inflation. Choose compounding that produces $1125.51 to the nearest cent.
- Target: Starting principal = 1000 dollars; tolerance 0 dollars.
- Target: Nominal annual rate = 12 %; tolerance 0 %.
- Target: Years = 1 years; tolerance 0 years.
- Target: Annual inflation = 0 %; tolerance 0 %.
- Target: Nominal balance = 1125.51 dollars; tolerance 0.005 dollars.