Formula
Savings Goal Timeline Formula (Contributions + Growth)
The calculator combines your starting balance, ongoing contributions, and any optional compounding to estimate how a balance might grow over time. Here’s the plain-language formula and one quick example so you can see what the tool is doing.
Published: December 22, 2025 · Updated: December 22, 2025 · By FinToolSuite Editorial
Run it in the calculator
Enter your numbers to see the same math applied to your goal.
Open the Savings Goal Timeline CalculatorQuick answer
Balance over time = growth on the starting balance + growth on the stream of contributions.
Contribution timing (start vs end of each period) nudges results because earlier deposits get a bit more time to grow.
See timing details: start vs end of period.
Disclaimer
Educational purposes only; not financial advice. Examples are illustrative; interest/returns vary and outcomes are not guaranteed. Fees, taxes, inflation, and rules differ by country and provider.
Define the variables
- P = starting balance (principal)
- PMT = contribution per period
- r = annual nominal rate (decimal, e.g., 0.03)
- n = compounding periods per year (e.g., 12 for monthly)
- t = years
- periods = n * t (total number of periods)
- periodic rate = r / n
Formula overview
A) Starting balance growth
FV_start = P * (1 + r/n)^(n*t)Applies compounding to the initial lump sum.
B) Contributions (end of period)
FV_contrib_end = PMT * [((1 + r/n)^(n*t) - 1) / (r/n)]Assumes deposits happen at the end of each period (ordinary annuity).
C) Contributions (start of period)
FV_contrib_start = FV_contrib_end * (1 + r/n)Adds one extra period of growth if deposits happen at the start (annuity due).
Worked example (illustrative)
Suppose P = £1,000; PMT = £100 monthly; r = 3% (0.03); n = 12; t = 2 years.
- Periodic rate = 0.03 / 12 ≈ 0.0025.
- Number of periods = 12 * 2 = 24.
- Starting balance growth: £1,000 * (1 + 0.0025)^24.
- Contributions (end of month): £100 * [((1 + 0.0025)^24 - 1) / 0.0025].
- If contributions are at the start of each month, multiply the contribution result by (1 + 0.0025).
For exact totals, drop these into the calculator: Savings Goal Timeline Calculator.
Special cases & notes
- If r = 0, the future value is just P + PMT * number_of_periods (pure saving, no growth).
- If you switch frequency (weekly vs monthly), n changes to match that cadence.
- Rate picks are illustrative; see rate assumptions for savings goals.
Contribution timing
End-of-period contributions (ordinary annuity) assume deposits land at the close of each period. Start-of-period contributions (annuity due) land at the beginning, giving one extra period of growth and a slightly higher future value.
Learn more: start vs end of period.
Map variables to the calculator
- P → starting balance field.
- PMT → contribution amount field.
- Frequency → sets n (weekly/biweekly/monthly).
- Rate → sets r (as a decimal or percent per the tool input).
- Horizon/goal → sets t (years or periods), or use time-to-goal mode if available.
Try your own numbers: Savings Goal Timeline Calculator.
FAQ
What formula does the calculator use?
It combines future value of a lump sum with future value of a contribution series, adjusted for timing (end vs start of period) based on the inputs you set.
What if the rate is 0%?
Then it’s pure saving: total = starting balance + contributions. The growth terms drop out.
What’s the difference between APR and APY here?
APR is nominal; APY reflects compounding. Use the calculator’s expected format. See the compound interest formula for more detail.
Does compounding frequency matter?
Yes. A higher n (e.g., monthly vs yearly) gives slightly more growth for the same nominal rate.
Start vs end of month—how much difference?
Start-of-period deposits get one extra period of growth, so the future value is a bit higher. See timing details.
Do fees, taxes, or inflation change the math?
They reduce net growth. A simple workaround is to lower the rate you use as an illustrative buffer.
Are results guaranteed?
No. Outputs are illustrative and depend on the inputs and assumptions you choose.
Where can I learn compound interest basics?
See the compound interest formula for a detailed walkthrough.
Try your own inputs
Plug in your numbers and compare monthly vs weekly saving.
Open the Savings Goal Timeline Calculator