# How will my savings grow?

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.

- Page: https://www.acalculator.org/finance/savings-calculator
- JSON spec: https://www.acalculator.org/finance/savings-calculator.json
- Version: 341b489a1422

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| initial | Initial deposit | The amount in the account at the start. |
| monthly | Deposit each month | The amount added at the end of every month. |
| apy | APY (annual percentage yield) | The yearly yield the bank quotes, with compounding included. A balance left for a year grows by exactly this percent. |
| years | For how long? (years) | How many years you save. |
| goal | Savings goal | A target balance. The calculator shows when you reach it and the deposit that reaches it in time. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| balance | You’ll have | The balance at the end of the last month. |
| deposits | Your deposits | The initial deposit plus every monthly deposit. |
| interest | Interest | All the interest earned: the final balance minus your deposits. |
| firstYear | Interest in the first year | The interest earned in the first 12 months. |
| goalMonths | Months to reach your goal | The first month whose end balance is at or above the goal, counted from the start. 0 when the initial deposit already reaches it. |
| needed | Monthly deposit to reach your goal in time | The deposit each month that makes the final balance equal the goal, or 0 if no deposit is needed. |

## 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).

## Assumptions

- 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.

## Worked examples

1. initial = $10,000.00, apy = 4%, years = 1 gives balance = $10,400.00, interest = $400.00, firstYear = $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 = $0.00, monthly = $200.00, apy = 5%, years = 10 gives balance = $30,872.63, deposits = $24,000.00, interest = $6,872.63. Source: future value of monthly deposits, hand calculation in content.mdx.
3. initial = $1,000.00, monthly = $100.00, apy = 0%, years = 5, goal = $5,000.00 gives balance = $7,000.00, goalMonths = 40, needed = $66.67. Source: hand calculation in content.mdx: 1,000 + 40 × 100 = 5,000; (5,000 − 1,000) ÷ 60.
4. initial = $0.00, monthly = $100.00, apy = 3%, years = 2, goal = $10,000.00 gives balance = $2,469.32, needed = $404.97. Source: hand calculation in content.mdx.

## FAQ

### 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.

## Sources

- Consumer Financial Protection Bureau, Regulation DD (Truth in Savings), 12 CFR 1030, Appendix A: annual percentage yield calculation. https://www.consumerfinance.gov/rules-policy/regulations/1030/a/
- FDIC, Deposit insurance: $250,000 per depositor, per insured bank, for each account ownership category. https://www.fdic.gov/resources/deposit-insurance
- Internal Revenue Service, About Form 1099-INT, Interest Income. https://www.irs.gov/forms-pubs/about-form-1099-int
- U.S. Securities and Exchange Commission, Investor.gov savings goal calculator. https://www.investor.gov/financial-tools-calculators/calculators/savings-goal-calculator