How the savings calculator works
A savings goal comes down to one of two questions, and the calculator answers either:
- Monthly amount: you know the goal and the deadline, and want the deposit that gets you there. The deposit is rounded up to the next cent, so the last month always reaches the goal.
- Time to goal: you know what you can put away each month, and want to know when the balance first reaches the goal.
Savings accounts advertise an annual percentage yield (APY), the yearly return including the effect of compounding. The calculator turns it into the monthly rate that compounds to exactly that APY over 12 months, adds that month’s interest to the balance, rounds it to the cent as a bank does, and then adds your deposit at the end of the month.
This is a goal planner for cash savings — an emergency fund, a down payment, a car. To see how an invested lump sum and regular contributions could grow over decades, use the investment calculator.
Savings formulas
After n months, savings P plus a deposit D at the end of every month grow to:
FV = P × (1 + m)ⁿ + D × ((1 + m)ⁿ − 1) ÷ m
- P
- current savings
- D
- monthly deposit
- m
- monthly rate: (1 + APY)^(1/12) − 1, so 4% APY gives m = 0.0032737
- n
- number of months
- G
- your savings goal
Setting FV equal to the goal G and solving for the deposit gives the monthly amount:
D = (G − P × (1 + m)ⁿ) × m ÷ ((1 + m)ⁿ − 1)
Solving for n instead gives the number of months:
n = ln((G × m + D) ÷ (P × m + D)) ÷ ln(1 + m)
A fractional result is rounded up, because the goal is only reached once that month’s deposit is in. With no interest (m = 0) both formulas become simple division: D = (G − P) ÷ n and n = (G − P) ÷ D.
Worked example
You want $20,000 in 3 years. You already have $2,000 in a savings account paying 4% APY.
- Monthly rate: 1.04^(1/12) − 1 = 0.0032737
- Growth over 36 months: 1.0032737³⁶ = 1.124864 (the same as 1.04³)
- Your $2,000 grows to $2,000 × 1.124864 = $2,249.73 on its own
- Monthly deposit: ($20,000 − $2,249.73) × 0.0032737 ÷ 0.124864 = $465.386, rounded up to $465.39
Over the 36 months you deposit $16,754.04 and earn $1,246.16 in interest, finishing with $20,000.20.
The other way round: if you can only save $500 a month, n = ln((20,000 × 0.0032737 + 500) ÷ (2,000 × 0.0032737 + 500)) ÷ ln(1.0032737) = 33.67, so you reach the goal with the 34th deposit — 2 years and 10 months — with $20,186.25 in the account.
Things to keep in mind
- Savings rates move. Most savings and money market accounts pay a variable rate that can change at any time. Re-run the numbers when your rate changes.
- Interest is taxable. In the US, interest credited to an account you can withdraw from without penalty is taxable income for that year, even if you leave it in the account.
- Inflation eats into cash. A goal set in today’s prices, such as a car, may cost more by the time you reach it. Set the goal a little higher for longer deadlines.
- Deposit insurance. Deposits at an FDIC-insured bank are insured to at least $250,000 at each bank; large goals may call for more than one bank.
- Interest compounds on interest. The longer the deadline and the higher the rate, the more of the goal comes from interest. The compound interest calculator shows that effect on its own, and the simple interest calculator shows growth without it.
Why APY and not the interest rate?
APY already includes compounding, so two accounts can be compared directly even if one compounds daily and the other monthly. If you only know a nominal rate compounded monthly, the APY is slightly higher: 4% compounded monthly is an APY of about 4.07%.
Frequently asked questions
How much should I save each month to reach my goal?
Divide the part of the goal you still need by the number of months, then subtract the help you get from interest. With $2,000 saved, a $20,000 goal in 3 years at 4% APY needs $465.39 a month, about $35 less than straight division would suggest.
What is the difference between APY and the interest rate?
The interest rate is the yearly rate before compounding; APY is what you actually earn in a year once interest is added to your balance and starts earning interest itself. US banks must disclose the APY on savings accounts, so it is the figure to compare and the one to enter here.
Does daily or monthly compounding change the result?
Not if you enter the APY. The APY already reflects how often the bank compounds, and the calculator uses the monthly rate that produces exactly that APY over a year. The only small difference is when interest shows up within the year.
Why is my final balance slightly above the goal?
In the monthly-amount mode the deposit is rounded up to the next cent so the goal is met. In the time mode the last full deposit usually takes the balance past the goal. Either way you finish at or just above your target.
What if I can’t reach the goal at all?
With no monthly deposit, a balance only grows if it earns interest and is above zero, so a zero deposit at 0% never reaches a higher goal. The calculator says so, and it also stops at 100 years, suggesting a larger deposit instead.
Sources
Last reviewed September 15, 2026