A savings plan grows in two parts: your starting balance compounding over time, and the steady stream of monthly deposits each compounding from the moment it lands. Together they give the future value FV = P(1+i)ⁿ + PMT·((1+i)ⁿ−1)/i. What makes saving powerful is that the interest itself earns interest — so the longer the horizon, the more the balance outpaces the simple sum of your deposits. The single biggest lever is time: starting early beats saving more later.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the future-value-of-an-annuity formula. Not financial advice.
The savings equations
The first term grows your initial deposit by the monthly compound factor (1+i)ⁿ. The second is the future value of an ordinary annuity — the standard formula for a series of equal end-of-month deposits, each compounding for the time remaining. Add them for the projected balance. Subtract everything you actually paid in (the initial deposit plus all the monthly contributions) to see how much of the final balance is interest. If the rate is 0%, FV is simply P + PMT·n.
Worked example — a 10-year plan
Scenario: You start with 1,000, add 200 a month, and earn 5% annual interest for 10 years.
The plan grows to about 32,703. You deposited 1,000 + 200 × 120 = 25,000, so roughly 7,703 is interest. Stretch the same plan to 20 years and it reaches about 84,919 (49,000 deposited) — the balance more than doubles while the deposits only roughly double, because the extra decade lets the earlier compounding compound again. That accelerating gap between balance and deposits is the whole point of saving early.
Frequently Asked Questions
FV = P(1+i)ⁿ + PMT·((1+i)ⁿ−1)/i. 1,000 + 200/mo at 5% for 10 yr ≈ 32,703.
FV − (P + PMT·n). In the example: 32,703 − 25,000 ≈ 7,703.
They compound for longer, and the returns earn returns. Time is the biggest lever.
Yes — annual rate ÷ 12, compounded monthly, deposits at month-end (ordinary annuity).
Raise the monthly contribution, extend the years, or earn a higher rate — test combinations.