RightFiguresA lump sum, compounded
The ending balance is:
A = P × (1 + r/n)^(n×t)
P is the initial principal, r is the annual rate as a decimal, n is how many times interest compounds in a year, and t is the number of years. A 5% rate is r = 0.05. Monthly compounding uses n = 12. Daily compounding uses 365 periods, not a leap-year calendar.
Investor.gov’s compound interest glossary describes interest that is added to the balance so later periods earn interest on that interest. Its compound interest calculator is a separate tool and can include contributions. This page does not. Deposits you make on a schedule belong on the savings growth calculator.
Rounding and the yield
The power is computed with extra guard digits and rounded half up to the nearest cent once, at the end. Intermediate periods are not rounded to cents. A result above $100,000,000,000.00 is rejected instead of shown as a shortened number.
The effective annual yield is (1 + r/n)^n − 1. It does not depend on the principal or the number of years. It rounds half up to 6 decimal places of a percent. At annual compounding it matches the rate you type. More frequent compounding produces a higher yield from the same nominal rate.
A $10,000 example
$10,000.00 at 5%, compounded monthly for 10 years, ends at $16,470.09. Interest earned is $6,470.09. The effective annual yield is 5.11619%.
The same $10,000 at 5% compounded annually for 10 years ends at $16,288.95, because the interest is added only once a year. At 0%, the ending balance stays $10,000.00 and the yield is 0%.
$100 at 10% compounded annually for 2 years ends at $121.00. Compounded semiannually for one year it ends at $110.25, and the yield is 10.25%.
What this leaves out
The rate does not change, and nothing is added or withdrawn. Taxes, fees and inflation are not modeled. A balance that would pass $100,000,000,000.00 is outside the supported range. For a loan payment, use the loan payment calculator.
Frequently asked questions
Does this include monthly deposits?
No. The principal is a single starting amount. Use the savings growth
calculator when you add a contribution every month.
Why is the yield higher than the rate I typed?
The rate is nominal. When interest compounds more than once a year, the
effective annual yield is (1 + r/n)^n − 1, which is higher than r.
Are the principal and rate sent to analytics?
No. Analytics may record that this calculator ran. The amounts and the rate
stay in the browser.
Sources & review
- Compound interest — U.S. Securities and Exchange Commission, Investor.gov
- Compound interest calculator — U.S. Securities and Exchange Commission, Investor.gov
Last reviewed: . The formula is reproduced above so you can check the math independently.
Educational estimate only. A bank or fund projection can use a different day count, rate or rounding rule.