Formulas and sources
Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.
Future value with monthly deposits
Simple and Goal Planning modes
- FV
- future value
- P
- initial deposit
- PMT
- monthly contribution
- r
- the yearly interest rate (APR) as a decimal: 5% is 0.05
- n
- compounding periods per year: 1, 2, 4, 12 or 365
- i
- monthly rate: (1 + r/n)^(n/12) - 1
- t
- time in years
Deposits are monthly at every compounding frequency, each growing at the monthly rate i. With Contribution Timing set to Start of Month, the PMT part is multiplied by (1+i). At a 0% rate, FV = P + PMT × 12 × t.
Source: Standard compound interest and annuity formula; no single publisher.
In today's money
Simple and Goal Planning modes, with Find Future Value in Goal Planning
- Real Value
- the balance in today's money
- FV
- future value, from the formula above
- inflation
- the yearly inflation rate you enter, as a decimal: 2% is 0.02
- t
- time in years
Source: Standard formula; no single publisher. The 2% starting rate matches the Federal Reserve's longer-run inflation goal [1], a target rather than a forecast.
Required monthly contribution
Goal Planning mode, with Find Contribution
- PMT
- the monthly contribution needed
- G
- savings goal
- P
- initial deposit
- i
- monthly rate: (1 + r/n)^(n/12) - 1
- t
- time in years
With Start of Month, the divisor is also multiplied by (1+i). No contribution is needed when the deposit alone reaches the goal. At a 0% rate the divisor is the number of months, 12 × t.
Source: Standard formula; no single publisher.
Years to reach a goal
Goal Planning mode, with Find Years to Goal
- t
- years to reach the goal
- G
- savings goal
- P
- initial deposit
- D
- the monthly contribution, PMT; times (1+i) with Start of Month
- i
- monthly rate: (1 + r/n)^(n/12) - 1
The answer is shown in whole years and months, rounded to the nearest month. At a 0% rate, t = (G - P) ÷ (12 × PMT). If the balance cannot reach the goal, the tool says so. ln is the natural logarithm.
Source: Standard formula; no single publisher.
Sources
- Board of Governors of the Federal Reserve System. Why does the Federal Reserve aim for inflation of 2 percent over the longer run? Last updated August 22, 2025.
What this calculator does not cover
- This models one account at a fixed yearly rate with a level monthly deposit. It does not account for tax on interest, rate changes, rates that depend on the balance, or deposit insurance limits.
- Inflation is one constant yearly rate. For market-linked growth, see the Investment Calculator.
Sources checked on .