Dated assumptions · transparent formulas
Compound Interest
Compound interest pays growth on past growth. This guide shows the formula behind it, a recurring-deposit example you can verify, and where simple interest falls short.
Educational calculator. Inputs stay in your browser. Historical ranges are not forecasts or investment advice.
Inputs
Estimate comparison
| Assumption | Rate | Nominal FV | Real FV |
|---|---|---|---|
| Lower estimate1-year Treasury constant maturity | 4.28% | $7,915.29 | $6,716.21 |
| Middle estimateS&P 500 rolling 30-year total-return median | 10.80% | $9,621.50 | $8,163.95 |
| Higher estimateS&P 500 rolling 30-year total-return 75th percentile | 12.04% | $9,996.02 | $8,481.74 |
Growth curve and yearly schedule
The same projection engine draws each estimate and feeds the collapsible year-by-year detail.
- Lower estimate
- Middle estimate
- Higher estimate
Show year-by-year detail
| Year | Opening | Deposits | Interest | Ending |
|---|---|---|---|---|
| 1 | $1,000.00 | $1,200.00 | $174.73 | $2,374.73 |
| 2 | $2,374.73 | $1,200.00 | $330.77 | $3,905.50 |
| 3 | $3,905.50 | $1,200.00 | $504.53 | $5,610.03 |
| 4 | $5,610.03 | $1,200.00 | $698.01 | $7,508.04 |
| 5 | $7,508.04 | $1,200.00 | $913.45 | $9,621.50 |
Rate assumptions and sources
Lower / Middle / Higher estimates · reviewed 2026-09-12
- Lower estimate
4.28%
- FRED: 1-Year Treasury Constant Maturity Rate (DGS1)
Retrieved 2026-09-12 · observation 2026-09-10
Dated benchmark snapshot.
- Middle estimate
10.80%
- Damodaran historical returns, 1928-2025
Retrieved 2026-09-12
Median of 69 overlapping 30-year S&P 500 total-return windows through 2025.
- Higher estimate
12.04%
- Damodaran historical returns, 1928-2025
Retrieved 2026-09-12
75th percentile of 69 overlapping 30-year S&P 500 total-return windows through 2025.
- Inflation: 3.34%
- FRED: Consumer Price Index for All Urban Consumers (CPIAUCSL)
Compound annual change from August 2016 to August 2026; user input can replace it.
The formula and what each piece does
For a lump sum, compound interest follows A = P × (1 + r/m)^(mt): the balance compounds at the periodic rate r/m for mt total periods. More compounding periods per year add slightly more growth at the same annual rate.
Recurring deposits add an annuity term: each contribution compounds for the number of periods remaining after it is made. End-of-period contributions compound one period less than beginning-of-period ones, which is why the timing choice moves the result.
Worked example: $200 a month for 10 years
Deposit $200 at the end of every month with no starting balance, a 7% annual return, and monthly compounding. After 10 years the projection is about $34,600: $24,000 of deposits plus roughly $10,600 of compound growth.
The return assumption dominates the growth slice. The same schedule reaches about $31,100 at 5% and $38,700 at 9%. At 2.5% inflation, the 7% result represents roughly $27,000 of current purchasing power after 10 years.
Verify any projection by checking three inputs separately: deposit size, compounding frequency, and timing. A result that surprises you usually comes from a monthly deposit entered as an annual one, or from compounding set to annual while deposits stay monthly.
Where simple interest and reality differ
Simple interest pays only on the original principal, so a 7% simple-interest balance grows by the same dollar amount every year while compound growth accelerates. Over 10 years the gap is modest; over 30 years it dominates the outcome.
Real accounts add frictions the formula ignores: fees reduce the effective rate, savings rates can change, and investment returns arrive in an unpredictable sequence. The calculator treats your inputs as fixed assumptions, which is exactly why comparing lower, middle, and higher rates matters more than trusting one number.