acalculator

How will my savings grow?

Enter your deposit, what you add each month, and the account’s APY. See your balance, the interest, and how long a goal takes.

Your numbers

Optional.
Banks quote this as APY. Rates can change.
Savings goal
Optional. For example an emergency fund.
You’ll have
$19,319.07

Saving $17,000.00 over 5 years at 4% APY grows to $19,319.07, of which $2,319.07 is interest.

Your deposits $17,000.00Interest $2,319.07
88% your deposits12% interest
Your deposits
$17,000.00
Interest
$2,319.07
Interest in the first year
$243.69
Months
60

You’ll have: $19,319.07. Saving $17,000.00 over 5 years at 4% APY grows to $19,319.07, of which $2,319.07 is interest.

How much of it is interest?

How does it grow?

What does each year look like?

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

Computes the balance of a savings account from its APY, a starting deposit, and monthly deposits, and how long it takes to reach a savings goal.

Example with the default inputs (Initial deposit $5,000.00, Deposit each month $200.00, APY (annual percentage yield) 4%, For how long? (years) 5): Saving $17,000.00 over 5 years at 4% APY grows to $19,319.07, of which $2,319.07 is interest.

Method: Each month, interest = balance × ((1 + APY)^(1/12) − 1), then the monthly deposit is added; the monthly deposit that reaches a goal G in n months is (G − P(1 + g)^n) × g ÷ ((1 + g)^n − 1).

  • The APY stays the same for the whole time. Savings rates can change at any time.
  • Interest is added monthly at the rate that gives exactly the APY over 12 months.
  • Deposits are made at the end of each month.
  • Tax on interest is not included.
  • This is an estimate for planning, not financial advice.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Initial deposit $10,000.00, APY (annual percentage yield) 4%, For how long? (years) 1 gives You’ll have $10,400.00, Interest $400.00, Interest in the first year $400.00.Source: APY definition in Regulation DD (12 CFR 1030, Appendix A): a one-year balance earns exactly the APY; hand calculation in content.mdx
  2. Initial deposit $0.00, Deposit each month $200.00, APY (annual percentage yield) 5%, For how long? (years) 10 gives You’ll have $30,872.63, Your deposits $24,000.00, Interest $6,872.63.Source: future value of monthly deposits, hand calculation in content.mdx
  3. Initial deposit $1,000.00, Deposit each month $100.00, APY (annual percentage yield) 0%, For how long? (years) 5, Savings goal $5,000.00 gives You’ll have $7,000.00, Months to reach your goal 40, Monthly deposit to reach your goal in time $66.67.Source: hand calculation in content.mdx: 1,000 + 40 × 100 = 5,000; (5,000 − 1,000) ÷ 60
  4. Initial deposit $0.00, Deposit each month $100.00, APY (annual percentage yield) 3%, For how long? (years) 2, Savings goal $10,000.00 gives You’ll have $2,469.32, Monthly deposit to reach your goal in time $404.97.Source: hand calculation in content.mdx

How the balance is worked out

The calculator runs month by month. The APY (as a decimal) becomes a monthly rate:

g = (1 + APY)^(1/12) − 1

so 12 months of interest equal exactly the APY. Each month, interest = balance × g is added, then the monthly deposit is added at the end of the month. An empty monthly deposit counts as $0.

The results:

  • You’ll have is the balance after the last month.
  • Your deposits is the initial deposit plus every monthly deposit. Interest is the balance minus your deposits.
  • Interest in the first year adds the interest of the first 12 months.

With an initial deposit P, a monthly deposit D, and n months, the balance is P × (1 + g)^n + D × ((1 + g)^n − 1) ÷ g (or P + D × n when the APY is 0).

Savings goal G.

  • Months to reach your goal is the first month m (1, 2, …) whose end balance is at or above G. It is 0 if the initial deposit is already at least G, and it is left out if the balance does not reach G within the time you chose.
  • Monthly deposit to reach your goal in time is the deposit that makes the final balance equal G: (G − P × (1 + g)^n) × g ÷ ((1 + g)^n − 1), or (G − P) ÷ n when the APY is 0. It is $0 if the initial deposit alone reaches G.

Assumptions

  • The APY stays the same for the whole time.
  • Tax on interest is not taken out.
  • This is an estimate for planning, not financial advice.

Worked examples by hand

$10,000 for one year at 4.00% APY. g = 1.04^(1/12) − 1 = 0.0032737, and 12 months give 10,000 × 1.04 = $10,400: $400 of interest, exactly the APY.

$200 at the end of every month at 5% APY for 10 years, from $0. g = 1.05^(1/12) − 1 = 0.0040741, and (1 + g)^120 = 1.05^10 = 1.628895. Balance = 200 × 0.628895 ÷ 0.0040741 = 200 × 154.3632 = $30,872.63. Your deposits are 120 × 200 = $24,000, so the interest is $6,872.63.

$1,000 plus $100 a month at 0% for 5 years, goal $5,000. After m months the balance is 1,000 + 100m, which first reaches $5,000 at m = 40. The balance after 60 months is $7,000. To reach $5,000 in exactly 60 months you would need (5,000 − 1,000) ÷ 60 = $66.67 a month.

$100 a month at 3% APY for 2 years, goal $10,000. g = 1.03^(1/12) − 1 = 0.0024663, and (1 + g)^24 = 1.03^2 = 1.0609. Balance = 100 × 0.0609 ÷ 0.0024663 = $2,469.32, so the goal is not reached. The deposit that reaches $10,000 in 24 months is 10,000 × 0.0024663 ÷ 0.0609 = $404.97 a month.

Other questions people ask

What is APY?

APY (annual percentage yield) is the yearly return of a savings account with compounding included. US banks must quote it under the Truth in Savings rules (Regulation DD). If you leave $10,000 in an account at 4.00% APY for a year, you have $10,400 at the end, however often the bank adds interest.

What is the difference between APY and the interest rate?

The interest rate (APR) does not include compounding; APY does. An account that pays 3.93% interest added monthly has an APY of about 4.00%, because each month’s interest earns interest too. Enter the APY here, since that is the number banks must show.

How long will it take to reach my savings goal?

Enter your goal under "Savings goal". The calculator shows the first month your balance reaches it. It also shows the monthly deposit that would reach the goal by the end of the time you chose.

Is a high-yield savings account safe?

Deposits at an FDIC-insured bank are insured up to $250,000 per depositor, per bank, for each account ownership category. Check that the bank is FDIC-insured (or NCUA-insured for a credit union) before you open an account.

Is the interest taxed?

In the US, savings interest is usually taxable income in the year it is paid, and the bank reports it on Form 1099-INT when it is $10 or more. The calculator does not take tax out, so what you keep after tax is a little less.

Will my rate stay the same?

Probably not. Savings account rates are variable, and banks can change them at any time. The calculator assumes the same APY for the whole time, so treat the result as an estimate.