Future Value Calculator

Calculates the future value of either a single lump sum or a recurring contribution stream, given an interest rate and time horizon. For a lump sum, FV = PV × (1 + r)ⁿ. For periodic contributions, FV = PMT × [((1 + r)ⁿ − 1) / r].

Compounding frequency (annual, monthly, daily) is configurable.

Future value compounds at a rate determined by the periodic interest rate and the number of compounding periods. The single-payment formula multiplies by (1 + r)ⁿ where r is the rate per period and n is the number of periods. The annuity formula sums a geometric series of growing contributions. Continuous compounding uses FV = PV × e^(rt), the limit as compounding frequency approaches infinity, and produces marginally higher results than daily compounding (about 0.001% more per year of holding period at typical rates).

A worked example: $10,000 invested at 7% annual return for 30 years grows to $76,123 with annual compounding ($10,000 × 1.07³⁰). With monthly compounding at the same nominal rate, it grows to $80,851. The Rule of 72 is a useful mental shortcut: dividing 72 by the annual rate gives the approximate doubling time. At 7%, money doubles every 10.3 years. At 10%, every 7.2 years. The rule slightly underestimates at low rates and slightly overestimates at very high rates but gives a useful range for any plausible investment scenario.

The annuity calculation answers a different question: how does a stream of contributions grow? $500 monthly contributions for 30 years at 7% (compounded monthly) grows to $610,672 in nominal terms. Total contributed: $180,000. Compound growth: $430,672, more than double the principal. This is the saving-from-paycheck pattern that underlies most retirement planning, and the cost of starting late is steep: the same $500/month started at age 35 instead of 25 ends with $216,580 less at 65.

Limitations and assumptions are real. The formula assumes a constant rate, which is not how markets actually behave; sequence-of-returns risk is the technical name for the phenomenon that two paths with the same average return can produce dramatically different outcomes if the order of returns differs. Inflation reduces real purchasing power; nominal future value of $1 million in 30 years at 3% inflation is a real $412,000 in present-day purchasing power. Most retirement planners use real (inflation-adjusted) returns of 4-5% for conservative projections rather than the higher historical nominal averages, which produces tighter but more honest estimates.

For practical planning, the right rate depends on portfolio composition. A US-equity-heavy 401(k) historically averages 6-7% real return; a balanced portfolio (60/40 stocks/bonds) returns 4-5% real; cash savings preserve about 0% real after inflation in normal rate environments. Adjusting the calculator's input rate to match the actual asset mix gives more accurate projections than using a single canonical figure.