Compound Interest Calculator

Compound interest at a glance#

A compound interest calculator works out the future value of a deposit when interest is earned on both the principal and the interest already added. It uses the formula A = P(1 + r/n)^nt, where A is the future value, P is the principal, r is the annual rate as a decimal, n is how many times interest compounds per year, and t is the number of years. The interest earned is A minus P.

Worked example: put $1,000 (P) into an account paying 5% a year (r = 0.05), compounded once a year (n = 1), for 10 years (t = 10). Then A = $1,000 x (1 + 0.05/1)^{1 x 10} = $1,000 x 1.05¹⁰ = $1,628.89, so the interest is $1,628.89 minus $1,000, which is $628.89.

Here is how that same $1,000 at 5% compounded annually grows over time:

To calculate compound interest by hand, divide the annual rate by the number of compounding periods, add 1, raise that to the power of n times t, then multiply by the principal. Compounding more often, such as monthly instead of annually, raises the result slightly because interest is added sooner.

Enter your principal, rate, compounding frequency and term in the calculator above for the exact future value and interest. Results assume the rate stays fixed and no deposits or withdrawals are made, so a real account with rate changes or contributions will differ.

How compounding frequency changes the result#

Compounding frequency (n) is how often interest is added back to the balance. The more often it compounds, the sooner interest starts earning interest, so the final figure is slightly higher. Put $5,000 into an account paying 5% a year for 10 years: compounded once a year it grows to $8,144.47, but compounded monthly (n = 12) it grows to $8,235.05. That is about $90 more for the same rate and term, purely from compounding sooner.

The annual percentage yield (APY) folds frequency into a single number, so you can compare accounts fairly. An account at 5% compounded monthly has an APY of about 5.12%, while 5% compounded annually has an APY of exactly 5%. When two accounts quote the same nominal rate, the one that compounds more often pays more.

Contributions and time#

The plain A = P(1 + r/n)^nt formula assumes one deposit and no further additions. If you add money regularly, each contribution compounds for the time it stays in the account, so deposits made early are worth more at the end than deposits made later. Time is the bigger lever than rate for most savers: a smaller balance left for 30 years often beats a larger one left for 10.

Compound interest and simple interest agree after a single period, then separate. Simple interest pays only on the original principal, so $1,000 at 5% earns a flat $50 every year. Compound interest pays on principal plus accumulated interest, so the yearly gain grows: $50 in year one, then more each year after.

Compound interest questions#

What is compound interest?#

Compound interest is interest calculated on both the principal and the interest already added. Because each period earns interest on a larger balance, the total grows faster over time than simple interest, which is calculated on the principal alone.

How do I calculate compound interest by hand?#

Use A = P(1 + r/n)^nt. Divide the annual rate by the number of compounding periods, add 1, raise the result to the power of n times t, then multiply by the principal. Subtract the principal to get the interest earned.

What is the difference between compounded monthly and compounded daily?#

Daily compounding adds interest every day; monthly adds it once a month. Daily compounds on a slightly larger balance each step, so it pays a little more, but at typical rates the gap between daily and monthly is small, often a few dollars per $1,000 per year.

How much does compounding frequency matter?#

Less than the rate or the term. At 5% on $5,000 for 10 years, switching from annual to monthly compounding adds about $90. Doubling the term or raising the rate by a point changes the result far more.

What is APY?#

Annual percentage yield is the effective yearly rate after compounding is included. It lets you compare accounts with different compounding frequencies on equal terms. A 5% rate compounded monthly has an APY of about 5.12%.

Does compound interest apply to loans too?#

Yes. On a loan or credit card, compounding works against you: unpaid interest is added to the balance and then charged interest itself. The same formula applies, but the growing balance is money you owe rather than money you earn.