Annuities and savings Updated November 2026

Monthly deposit for a savings goal

To find the regular deposit that reaches a future target, rearrange the annuity future value formula: PMT = FV x r / ((1 + r)^n - 1), where r is the rate per period and n the number of deposits. In Excel use =PMT(rate, nper, 0, -goal). Higher returns or more time lower the deposit.

Syntax

PMT = FV x r / ((1 + r)^n - 1)

Part	What it is
`FV`	The savings target
`r`	Interest rate per period (annual rate / 12 for monthly)
`n`	Number of deposits

Examples

Goal 10,000 in 5 years, 6% a year, monthly deposits
PMT = 10,000 x 0.005 / (1.005^60 - 1)

Result: PMT = 143.33 per month

Excel: =PMT(6%/12, 60, 0, -10000)

Goal 50,000 in 10 years at 4.8% a year (0.4% monthly)
PMT = 50,000 x 0.004 / (1.004^120 - 1)

Result: PMT = 325.45 per month

Goal 100,000 in 10 years, 7% a year, yearly deposits
PMT = 100,000 x 0.07 / (1.07^10 - 1)

Result: PMT = 7,237.75 per year

Excel: =PMT(7%, 10, 0, -100000)

Common mistakes

Dividing the goal by the number of months (10,000 / 60 = 166.67) ignores interest and overstates the deposit needed.
Using the annual rate with monthly deposits; the rate must be per deposit period.
Starting with an existing balance and forgetting to subtract its future value from the goal, or in Excel forgetting to enter it as the pv argument.

Practice Monthly deposit for a savings goal

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

Monthly saving to reach a goalYou want $15,000 in 30 years. Your account earns 3.25% APR, compounded monthly. How much must you deposit at the end of each month?
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.
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?

Questions

How do I account for money I already have saved?

Reduce the goal by the future value of the starting balance, or in Excel pass it as pv: =PMT(6%/12, 60, -2000, -10000) gives the monthly deposit when 2,000 is already saved.

What if deposits are made at the start of each month?

Add type 1 in Excel, =PMT(6%/12, 60, 0, -10000, 1), or divide the ordinary result by (1 + r). The deposit falls slightly, to 142.62.

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.
How long savings will lastHow many months a balance lasts with fixed withdrawals: n = -ln(1 - PV x r / PMT) / ln(1 + r). Retirement examples, Excel NPER and the withdrawal that lasts.
Future valueHow to calculate the future value of a lump sum with FV = PV x (1 + r)^n, step-by-step examples, the Excel FV function with its sign convention, and 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.