Interest basics Updated November 2026

Future value

The future value of a single amount is FV = PV x (1 + r)^n, where PV is the amount today, r the interest rate per period and n the number of periods. It tells you what today's money grows to after compounding. For monthly compounding use r/12 and n in months.

Syntax

FV = PV x (1 + r)^n

Part	What it is
`PV`	Present value, the amount today
`r`	Interest rate per period, as a decimal
`n`	Number of periods

Examples

PV = 500, r = 4% per year, n = 5 years
FV = 500 x 1.04^5

Result: FV = 608.33

Excel: =FV(4%, 5, 0, -500)

PV = 10,000, 6% compounded monthly, 10 years
FV = 10,000 x (1 + 0.06/12)^120

Result: FV = 18,193.97

Excel: =FV(6%/12, 120, 0, -10000)

Reverse it: what rate turns 10,000 into 20,000 in 8 years?
r = (20,000 / 10,000)^(1/8) - 1

Result: r = 9.05%

Excel: =RATE(8, 0, -10000, 20000)

Common mistakes

Mismatching rate and periods (annual rate with monthly periods) is the most common error; both must be per the same period.
Excel FV returns a negative value if PV is entered as positive; enter -PV, or wrap the formula in -FV(...).
Using the future value formula for a stream of deposits: for regular payments use the annuity future value formula or FV with the pmt argument.

Practice Future value

These drills check your answer on live data, free, no account needed.

Future value of a lump sumYou deposit $1,500 in an account that earns 3.25% per year, compounded annually. You make no other deposits or withdrawals. How much is in the account after 30 years?
Return needed to reach a goalYou have $2,000 today and want $3,000 in 5 years, with no further deposits. What annual return, compounded annually, gets you there exactly?
Years to reach a goalYou invest $2,000 at 10% per year, compounded annually. How many years will it take to grow to $3,000? Give the exact figure to 2 decimals.

Questions

What is the future value formula in Excel?

=FV(rate, nper, pmt, [pv], [type]). For a lump sum set pmt to 0: =FV(4%, 5, 0, -500) returns 608.33.

How do I find the number of years to reach a future value?

n = ln(FV / PV) / ln(1 + r). Doubling at 8% takes ln(2) / ln(1.08) = 9.01 years. In Excel: =NPER(8%, 0, -1, 2).

Present valueHow to calculate present value with PV = FV / (1 + r)^n, what discounting means, examples with yearly and quarterly rates, the Excel PV function and mistakes.
Compound interestThe compound interest formula A = P(1 + r/n)^(nt), what each symbol means, examples for yearly and monthly compounding, the Excel FV function and errors.
Annuity formula (future value)The future value of an ordinary annuity is PMT x ((1 + r)^n - 1) / r. Examples for yearly and monthly deposits, the Excel FV function and common errors.
Rule of 72The rule of 72 estimates doubling time as 72 divided by the rate. Examples at 6%, 9% and 18%, how accurate it is, the exact ln(2) formula and Excel NPER.