Savings Calculator
See how savings grow with monthly deposits at your APY, or find how much to save each month to reach a goal.
= 4.4020% APR compounded daily
1 to 100 years
Deposits land at the end of each month. In year one, interest on the starting balance is $ 225.00 ($ 5,000.00 × 4.50% APY).
Year-by-year breakdown
| Year | Deposits ($) | Interest ($) | Balance ($) |
|---|---|---|---|
| Start | – | – | 5,000.00 |
| Year 1 | 2,400.00 | 274.11 | 7,674.11 |
| Year 2 | 2,400.00 | 394.44 | 10,468.55 |
| Year 3 | 2,400.00 | 520.19 | 13,388.74 |
| Year 4 | 2,400.00 | 651.60 | 16,440.34 |
| Year 5 | 2,400.00 | 788.92 | 19,629.26 |
Shows how a savings account grows from a starting balance and a regular deposit, or works backwards from a goal: the deposit that reaches it in time, or how long your deposit takes. The rate can be entered as an APY, as banks advertise it, or as an APR with its compounding, and an introductory rate can run before the ongoing one. It works in any currency.
How to use it
- Work out — the end balance after a time, the deposit a goal needs, or the time to reach a goal at your deposit. Switching keeps the last answer in the field that takes its place.
- Deposit — weekly, every two weeks, monthly or yearly, landing at the end of each period.
- Interest rate — 0% to 50%, as an APY or an APR. An APR needs its compounding (daily, monthly, quarterly or yearly); an APY already includes it. The other form shows under the field.
- Reach the goal — in a number of years or months, or by a date. A date counts the full months from today; a part month left over is not counted.
- Introductory rate — a promotional rate for up to 120 months, after which the interest rate applies.
- Deposits rise each year — by a percentage, so each year's deposits are that much more than the last.
How it works
An APY (annual percentage yield) is what a year of interest comes to with its compounding included: 4.5% APY on 5,000 earns $ 225.00 in a year, however often the bank compounds. So the calculator grows the balance by (1 + APY)^(1/p) − 1 in each of the p deposit periods a year, and never compounds an APY again. An APR (the nominal rate) is converted to its APY first. Feeding an APY into a field that compounds it again overstates the interest: 5% treated as a rate compounded monthly gives 5.12%, not 5%.
Each year's figures are rounded to the cent from running totals, so the rows add up to the totals shown. The line under the result checks year one: the starting balance times the APY is the interest it earns in the first year.
APY = (1 + APR ÷ n)ⁿ − 1
APR = n × ((1 + APY)^(1/n) − 1)
Balance = S × (1 + i)ᵏ + D × ((1 + i)ᵏ − 1) ÷ i, with i = (1 + APY)^(1/p) − 1
S = starting balance, D = deposit, k = deposits, p = deposits a year, n = compounding periods a year
Examples
5,000 plus 200 a month at 4.5% APY for 5 years
The balance reaches $ 19,629.26: $ 17,000.00 of your money and $ 2,629.26 interest. In year one the starting balance earns $ 225.00, which is 5,000 × 4.5%. The same 4.5% APY is a 4.4020% APR compounded daily.
Reaching 20,000 in three years
From 5,000 at 4.5% APY, with Deposit needed and the goal in 3 years, the monthly deposit is $ 372.11. With no interest it would be $ 416.67: interest does $ 1,604.31 of the work.
An introductory rate, then a lower one
10,000 at 5.5% APY for 6 months, then 4% APY, earns $ 474.73 in the first year, against $ 400.00 at 4% throughout. Over the year that comes to 4.75% on the balance.
Rules and sources
In the United States, Regulation DD (Truth in Savings) defines the APY banks must disclose: the interest a year earns on the principal, assuming all interest stays in the account and nothing else is paid in or taken out, worked as 100 × ((1 + interest ÷ principal)^(365 ÷ days) − 1). For an account without a set term the year is 365 days, so the APY is simply the year's interest over the principal. An introductory rate is worked into the APY for the months it lasts, with the ongoing rate for the rest of the year.
A savings account's rate is usually variable: the bank can change it, so the result holds only while the rate does.
Sources
Reviewed
Frequently asked questions
See also
- CD Calculator — for a fixed-term deposit, with the early withdrawal penalty.
- Investment Calculator — for growth at an investment return, solving for any figure.
- FD Calculator — for an Indian fixed deposit.
- RD Calculator — for an Indian recurring deposit.