🚀 Future Value Calculator
Future Value Calculator — FV, Annuity & Growing Payments
Calculate how much a lump sum, regular deposits, growing contributions, or continuously compounded investment will be worth at a future date.
FV = PV × (1+r)ⁿ
Lump Sum
FV = PMT × [(1+r)ⁿ−1] / r
Annuity
FV = PMT×[(1+r)ⁿ−(1+g)ⁿ]/(r−g)
Growing Annuity
FV = PV × e^(rn)
Continuous
💰 Lump Sum FV
📅 Annuity FV
📈 Growing Annuity
♾️ Continuous Compounding
Future Value Calculator
Lump Sum · Annuity · Growing Annuity · Continuous
💰 Lump Sum
📅 Annuity
📈 Growing Annuity
♾️ Continuous
Single Investment
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%
yrs
Regular Deposits + Starting Balance
$
$
%
Growing Payments
$
%
%/yr
yrs
Continuous Compounding
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%
yrs
💡 Continuous compounding (FV = PV × e^(rn)) gives the theoretical maximum FV for a given rate. Compare it to discrete compounding above.
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Future Value
$0
Principal
$0
Interest Earned
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Total Return
📊 Investment Growth — Principal vs Interest Over Time
📊 FV Sensitivity — Different Interest Rates
How future value changes at different annual rates (your rate highlighted)
| Annual Rate | Future Value | Interest Earned | Total Return |
|---|
📋 Growth Schedule
| Period | Opening Balance | Payment | Interest Earned | Closing Balance (FV) |
|---|
Future Value Formulas
- Lump Sum:
FV = PV × (1+r)^n - Ordinary Annuity:
FV = PV×(1+r)^n + PMT×[(1+r)^n−1]/r - Annuity Due: Ordinary FV × (1+r)
- Growing Annuity:
FV = PMT × [(1+r)^n − (1+g)^n] / (r−g) - Continuous Compounding:
FV = PV × e^(r×n)
FV Comparison Across Compounding Frequencies
$1,000 at 6% for 10 years:
| Compounding | FV | Interest Earned |
|---|---|---|
| Annual (1×/yr) | $1,790.85 | $790.85 |
| Semi-Annual (2×/yr) | $1,806.11 | $806.11 |
| Quarterly (4×/yr) | $1,814.02 | $814.02 |
| Monthly (12×/yr) | $1,819.40 | $819.40 |
| Daily (365×/yr) | $1,822.03 | $822.03 |
| Continuous | $1,822.12 | $822.12 |
Power of Regular Contributions
| Scenario | PV | PMT | Rate | Years | FV |
|---|---|---|---|---|---|
| Lump sum only | $1,000 | $0 | 6% | 10 | $1,791 |
| Deposits only | $0 | $100/mo | 6% | 10 | $16,388 |
| Both | $1,000 | $100/mo | 6% | 10 | $18,179 |
| Higher rate | $1,000 | $100/mo | 10% | 10 | $21,037 |
| Longer term | $1,000 | $100/mo | 6% | 30 | $102,274 |
Frequently Asked Questions
Future value (FV) is the amount an investment will grow to at a specified future date, given a rate of return and compounding rules. For a lump sum: FV = PV × (1+r)^n. For regular deposits: FV = PV×(1+r)^n + PMT×[(1+r)^n−1]/r. FV is the reverse of present value — it converts today's money into tomorrow's money by applying compound growth.
Ordinary annuity: payments at the END of each period (mortgages, bonds, most savings accounts). FV = PMT × [(1+r)^n−1]/r. Annuity due: payments at the START of each period (leases, insurance). FV(due) = FV(ordinary) × (1+r). Because annuity due payments are invested one period earlier, they earn one extra compounding period, resulting in a slightly higher FV.
A growing annuity has payments that increase at a constant growth rate g each period. Formula: FV = PMT × [(1+r)^n − (1+g)^n] / (r−g). Example: annual deposits starting at $1,000 that grow by 3% per year, invested at 7%. This models salary escalation — each raise is automatically invested, compounding faster than a flat contribution.
Continuous compounding applies interest an infinite number of times per year: FV = PV × e^(r×n). It produces the maximum possible FV for a given nominal rate. At 6% for 10 years: annual = $1,790.85; continuous = $1,822.12. Used in mathematical finance, options pricing (Black-Scholes), and some derivatives. Practical difference from daily compounding is negligible for most savers.
More frequent compounding yields slightly higher FV. At 6% for 10 years on $1,000: annual = $1,790.85; monthly = $1,819.40; daily = $1,822.03. The difference is small for typical savings rates but grows with larger principals, higher rates, and longer terms. When comparing accounts, compare APY (not APR) — APY already accounts for compounding frequency.