Future value formula

The future value of a lump sum:

FV = PV × (1 + r/n)^(n×t)
where:
  PV = present value (initial investment)
  r  = annual interest rate (decimal)
  n  = compounding periods per year
  t  = years

The power of compound interest

Einstein is often (possibly apocryphally) credited with calling compound interest the "eighth wonder of the world." Even modest differences in return rate or time horizon have dramatic effects on long-term wealth:

$10,000 invested at…	After 20 years	After 30 years
5% annually	$26,533	$43,219
7% annually	$38,697	$76,123
10% annually	$67,275	$174,494

Rule of 72

A quick estimate: divide 72 by your annual return rate to get the approximate number of years to double your money. At 6%, your money doubles in approximately 72 ÷ 6 = 12 years.

Real vs. nominal value

The FV formula produces nominal (not inflation-adjusted) values. $10,000 invested at 7% nominal for 30 years becomes ~$76,123 in nominal terms, but at 2% annual inflation, that amount has the purchasing power of approximately $42,000 in today's dollars. To calculate in real terms, subtract inflation from the return rate: at 7% nominal minus 2% inflation, use 5% real return, giving ~$43,219 in real dollars.

Tax-advantaged accounts

The FV formula applies differently depending on account type:

Roth IRA: contributions are after-tax; all growth and qualified withdrawals are tax-free. The full FV amount is spendable.
Traditional 401(k) / IRA: contributions are pre-tax; the full balance grows tax-deferred but withdrawals are taxed as ordinary income. The after-tax FV = FV × (1 − marginal tax rate at withdrawal).

Regular contributions

For consistent periodic contributions (like monthly 401k contributions), use the future value of an annuity formula:

FV = PMT × ((1 + r)^n − 1) / r

where PMT is the periodic contribution, r is the rate per period, and n is the number of periods. This compounds every contribution separately over the remaining time horizon.