RightFiguresThe smallest deposit that reaches the target
This page starts from the balance you want and finds the smallest monthly contribution that gets there. It is not the savings growth calculator, which starts from a contribution you already chose and projects the ending balance.
Each month does two things, in this order:
- Credit interest on the balance at the start of the month. The monthly rate is the annual rate divided by 12. That interest rounds half up to the nearest cent.
- Add the monthly contribution after the interest. The contribution earns nothing until later months.
The search tries whole cents. A contribution qualifies when the ledger finishes at or above the target and no month-end balance is above $100,000,000,000.00. The result is the smallest such cent. One cent less stays short. Interest rounding can leave the ending balance above the target, because the balance can jump by more than one cent.
Investor.gov’s savings goal calculator also solves for a contribution toward a target. It does not have to use this monthly cent ledger, so its contribution can differ. The compound interest calculator grows one amount and does not take monthly deposits.
A $14,480.75 target
Start with $1,000.00, aim for $14,480.75, and use 4% for 5 years (60 months).
The smallest monthly contribution is $200.00. The ending balance is $14,480.75, contributions are $12,000.00, and interest is $1,480.75. A contribution of $199.99 ends at $14,480.09, which misses the target. This is the same ledger as the published savings-growth example, read in the other direction.
At 0%, a $1,000.00 start needs $200.01 a month for two years to pass a $5,800.01 target. That contribution ends at $5,800.24. $200.00 ends at $5,800.00 and is one cent short.
What this leaves out
The rate does not change, and the contribution does not change. There are no withdrawals, fees, taxes, or inflation. A result above $100,000,000,000.00 is rejected. If the starting balance already reaches the target, the contribution is $0.00 and the page still shows the balance after the years you entered, when that projection stays inside the limit.
Frequently asked questions
Why can the ending balance be above the target?
The contribution is a whole number of cents. Adding one cent can raise later
interest by a cent, so the ending balance can skip the exact target. The page
reports that gap.
Why might a bank show a different deposit?
A bank can use a
daily balance, a different day count, or rounding that is not half up to the
cent each month. This page always uses the annual rate divided by 12.
Sources & review
- Savings goal calculator — U.S. Securities and Exchange Commission, Investor.gov
- Compound interest calculator — U.S. Securities and Exchange Commission, Investor.gov
Last reviewed: . The formula is reproduced above so you can check the math independently.
Educational estimate only. The contribution is not a savings plan or a market return.