Dated assumptions · transparent formulas
Future Value Formula
Use this student reference to trace every calculator result back to lump-sum compounding, annuity timing, and inflation conversion.
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.
Future value formula with a worked lump-sum example
For one deposit with annual compounding, FV = PV × (1 + r)^n. PV is today’s starting balance, r is the annual rate as a decimal, and n is years. A $1,000 deposit at 5% for 10 years becomes $1,000 × 1.05^10 = $1,628.89.
If interest compounds monthly at a nominal 5% annual rate, use FV = $1,000 × (1 + 0.05/12)^120 = $1,647.01. Monthly compounding and annual compounding use different effective annual returns; do not mix a nominal rate with an effective APY.
Future value formula for regular and growing payments
For equal end-of-period deposits, FV = PV × (1 + i)^n + P × ((1 + i)^n − 1) / i. With $100 a month, zero opening balance, 5% nominal interest compounded monthly, and 10 years, i = 0.05/12 and n = 120, giving $15,528.23.
For payments at the beginning of each period, multiply only the payment term by (1 + i), not the opening-balance term. With zero interest, the payment term becomes P × n.
For annual payments that grow at g each year, the end-of-year payment term is P × ((1 + r)^n − (1 + g)^n) / (r − g). When r = g, it becomes P × n × (1 + r)^(n − 1). P is the first payment, not the final payment.
Core formula
For a lump sum, FV = PV × (1 + r/m)^(mt), where r is the nominal annual rate, m is compounding periods per year, and t is years.
For recurring payments, the calculator converts the annual rate to the contribution-period rate and applies beginning- or end-of-period timing explicitly.
Real future value is nominal future value divided by (1 + inflation rate)^years.