Compound Interest Calculator
Project the growth of a deposit with compound interest and optional monthly contributions, separating what you put in from interest earned.
Updated Formula covered by automated tests
Compound interest is what happens when the interest an account earns is added to the balance and then earns interest of its own. Over a few months the effect is barely visible; over decades it can account for most of the final balance. Enter a starting deposit, an annual rate, how often the interest is credited and an optional amount you add every month, and the tool shows the ending balance, the money you put in and the part that came from interest.
Savers use it to see what a certificate of deposit, a high-yield savings account or a long-term index fund holding might grow to, and to test how much difference an extra $50 a month or five more years would make. Because the starting deposit and the monthly additions are tracked separately, you can also see how much of the outcome depends on regular saving rather than on the rate.
The formula
- A
- Balance at the end of the period, in dollars
- P
- Starting deposit (principal) in dollars
- r
- Nominal annual interest rate as a decimal, so 7% is 0.07
- n
- Compounding periods per year: 1 annually, 4 quarterly, 12 monthly, 365 daily
- t
- Length of time in years
- C
- Amount added at the end of every month
- i
- Effective monthly growth rate implied by r and n; equal to r ÷ 12 for monthly compounding
- m
- Number of monthly contributions
The first term is the classic lump-sum formula: in each of the n × t periods the balance is multiplied by (1 + r/n). The second term is the future value of an ordinary annuity, the sum of every monthly deposit grown for the months it had left to earn. A deposit made at the end of the final month earns nothing, while the first one earns for m − 1 months.
When interest is credited quarterly or annually but you save monthly, the tool converts the quoted rate into the equivalent monthly rate i so that the deposits and the principal grow at the same effective annual yield. A 0% rate is handled as plain addition.
Worked example
Jordan puts $10,000 into an account that pays 7% a year compounded monthly and adds $200 at the end of every month for 10 years.
- 1 Monthly rate: 0.07 ÷ 12 = 0.0058333, over 120 months. Growth factor: (1.0058333)¹²⁰ = 2.00966.
- 2 Starting deposit: 10,000 × 2.00966 = $20,096.61.
- 3 Monthly deposits: 200 × (2.00966 − 1) ÷ 0.0058333 = $34,616.96.
- 4 Ending balance: 20,096.61 + 34,616.96 = $54,713.58.
- 5 Money put in: 10,000 + 200 × 120 = $34,000, so interest earned is 54,713.58 − 34,000 = $20,713.58.
Result: After 10 years Jordan has about $54,714, of which $20,714 is interest. The same plan with quarterly compounding ends slightly lower, at about $54,556.
Before you rely on the result
- Assumes the rate stays constant for the whole period and that contributions arrive at the end of each month. Deposits at the start of the month would grow a little more.
- Ignores taxes on interest, account fees and inflation, all of which reduce what the balance is really worth. A licensed financial adviser can help you plan with those included.
Frequently asked questions
How much does daily compounding beat monthly compounding?
Less than most people expect. At 5% for one year, $1,000 grows to $1,051.16 with monthly compounding and $1,051.27 with daily compounding, a difference of 11 cents. The rate itself and the time invested matter far more than the compounding frequency.
What is the difference between APR and APY on a savings account?
APR (or the nominal rate) is the r in the formula. APY is the yield after a full year of compounding, (1 + r/n)ⁿ − 1, so 5% compounded monthly is an APY of about 5.12%. US banks must quote APY on deposit accounts under the Truth in Savings rules. If you only know the APY, enter it with annual compounding.
How long does it take to double my money?
The rule of 72 gives a quick estimate: divide 72 by the annual rate in percent. At 7% that is about 10.3 years; the exact answer with annual compounding is ln 2 ÷ ln 1.07 = 10.24 years.
Can I use this for stock market returns?
Only as a rough illustration. Stocks do not pay a fixed rate; returns vary widely from year to year and can be negative. A constant average rate hides that variation and the order of good and bad years, which matters a great deal when you are adding or withdrawing money.
Sources
- Investor.gov (US SEC): Compound Interest Calculator (investor.gov)
- Consumer Financial Protection Bureau: Regulation DD (Truth in Savings) (consumerfinance.gov)