Future Value Formula
Reference for future value formulas FV = PV(1+r)^n for lump sums and FV = PMT[(1+r)^n-1]/r for annuities.
Covers compounding frequency and the Rule of 72.
The Formula
Future value calculates how much an investment made today will grow to at a specific point in the future. It accounts for the power of compound growth over time.
Variables
| Symbol | Meaning |
|---|---|
| FV | Future value (what the money will be worth later) |
| PV | Present value (the amount you invest today) |
| r | Interest rate per period (as a decimal) |
| n | Number of periods (usually years) |
Example 1
You invest $8,000 today at 7% annual return for 15 years.
PV = $8,000, r = 0.07, n = 15
FV = 8000 × (1 + 0.07)^15
FV = 8000 × (1.07)^15
FV = 8000 × 2.7590
FV = $22,072.00 — Your $8,000 grows to over $22,000 in 15 years.
Example 2
You put $25,000 in a fund earning 5% per year for 20 years.
PV = $25,000, r = 0.05, n = 20
FV = 25000 × (1 + 0.05)^20
FV = 25000 × (1.05)^20
FV = 25000 × 2.6533
FV = $66,332.50 — Your investment more than doubles over 20 years.
When to Use It
Use the future value formula when:
- Planning how much your savings will grow for retirement
- Comparing different investment options over the same time period
- Setting financial goals and determining how much to invest now
- Understanding the long-term impact of different interest rates
Key Notes
- Lump-sum formula: FV = PV × (1 + r)^n: A single investment grows exponentially. $10,000 at 7% for 30 years becomes $76,122. Small changes in r make enormous differences over long periods — this is the core of long-term investing.
- Annuity FV: FV = PMT × [(1+r)^n − 1] / r: The future value of equal periodic payments. Used to project a retirement account where contributions are made each year. An extra $1,000/year at 7% for 30 years adds ~$94,460 to the final balance.
- Continuous compounding: FV = PV × e^(rt): The theoretical limit of infinitely frequent compounding. At r=7%, continuous compounding gives FV/PV = e^(0.07t) vs (1.07)^t for annual — the difference is small but grows with time.
- Nominal vs real future value: FV from the formula is in future (nominal) dollars. To find real purchasing power, divide by (1 + inflation)^n. A 7% nominal return with 3% inflation gives a real return of approximately 4%.
- Applications: Future value calculations are used in retirement planning, education savings accounts, business investment decisions, and any scenario where money grows over time at a known rate.