The two questions
Without interest the answer is simple division: goal minus what you have, divided by months. Interest changes it because every deposit starts growing as soon as it lands, and so does the money you already have. The result is a smaller monthly deposit than plain division gives, and the difference grows with the rate and the length of time.
Balance after M months = P(1+i)^M + C x ((1+i)^M - 1) / i, with i = APR / 12, P = saved so far and C = monthly deposit. Deposit needed: C = (Goal - P(1+i)^M) x i / ((1+i)^M - 1). Months needed: M = ln((Goal x i + C) / (P x i + C)) / ln(1+i). Deposits are made at the end of each month, interest compounds monthly and the rate does not change.
A worked example
A student wants $12,000 in 24 months. They have $1,500 saved and the account pays 4.5% a year. The $1,500 grows to $1,640.99 over two years on its own, so the deposits must cover the remaining $10,359.01 including their own interest.
| Question | Inputs | Answer |
|---|---|---|
| Deposit needed | $12,000 goal, $1,500 saved, 4.5%, 24 months | $413.30 a month |
| Time to goal | Same goal, $300 a month | 32.4 months, so 33 deposits |
At $413.30 a month, total deposits are $9,919.25 and interest adds $580.75. At $300 a month the goal is reached during the 33rd month with a balance of $12,214.89, of which $814.89 is interest. The final deposit overshoots slightly, which is why the calculator shows the exact figure and the whole number of deposits.
Setting a realistic plan
Short goals earn little interest, so the rate matters less than the monthly habit. For a goal under two years, rounding up the deposit is the safest approach. Money you will need soon belongs in a savings account or similar, where the balance cannot drop, and not in investments that move up and down.
If the deposit looks too high, change one thing at a time: a longer timeline, a smaller goal or a head start from money you already have. The calculator tells you plainly when the goal has already been reached, and when no deposit and no interest means it never will be.
Common mistakes
- Using the APY and APR as if they were the same. This calculator takes an APR compounded monthly. Check what your account states.
- Counting on a rate that may drop. Savings rates change, so test a lower one.
- Forgetting that interest is taxable in many accounts, which trims the result slightly.
- Setting the goal in today's prices when it will cost more later, such as tuition or a car.
- Skipping a month and not adjusting. Rerun the numbers with the new balance and months left.
Estimate for learning, not financial advice. Inputs stay in your browser and are not sent or stored.