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Compound Interest Calculator
Calculate compound interest with the periodic formula or continuous growth, including a year-by-year table.
Starting amount in dollars, such as 1000
5 means 5%, not 0.05
1 is annual, 12 is monthly, and 365 is daily. Type any whole number from 1 to 525600, which is once a minute.
How long the money grows, such as 1 or 10
Enter a principal, an annual rate, compounds per year, and a time in years.
Enter a principal, an annual rate, compounds per year, and a time in years.
This compound interest calculator is for algebra and personal-finance classwork. Enter a principal, an annual percent rate, how many times a year interest is compounded, and a time in years. The page substitutes those numbers into A = P(1 + r/n)^(nt) and shows the accumulated amount and the interest earned. A continuous mode uses A = Pe^(rt). Presets cover annually, semiannually, quarterly, monthly, and daily compounding, and a year-by-year table shows how the amount grows.
The compound interest formula
Compound interest is interest earned on both the original principal and the interest already added. The periodic formula is A = P(1 + r/n)^(nt). A is the accumulated amount, principal plus interest. P is the principal, the starting amount of money. r is the annual interest rate written as a decimal, so a rate of 5% means r = 0.05, not 5. n is the number of times interest is compounded in one year. t is the time in years.
Divide the decimal rate by n, add 1, raise that result to the power nt, and multiply by P. The interest earned is A − P. For P = 1000, r = 0.05, n = 12, and t = 1, the substituted formula is A = 1000(1 + 0.05/12)^(12×1). Rounded to the nearest cent, A is about $1,051.16 and the interest is about $51.16.
Annual, monthly, quarterly, and daily compounding
n follows the schedule. Annually means n = 1, semiannually means n = 2, quarterly means n = 4, monthly means n = 12, and daily means n = 365. A typed n has to be a whole number from 1 to 525600, which is once a minute. Compounded annually, 1000 at 5% for 1 year is 1000 × 1.05 = 1050 exactly, so the amount is $1,050.00 and the interest is $50.00. Compounding more than once a year produces a slightly larger amount. The year-by-year table lists each year up to 30. Past that, the table stops and says so, while the amount above still uses the full time.
A rate of 0% leaves the principal unchanged, so A = P and the interest is 0. A time of 0 years does the same, because any positive base to the power 0 is 1 and e^0 is 1.
Interest compounded continuously
Continuous compounding is the limit of compounding more and more often. It does not use n. The compounded continuously formula is A = Pe^(rt), where e is the base of the natural logarithm. For P = 1000, r = 0.05, and t = 1, A = 1000e^(0.05×1), which is about $1,051.27. That decimal does not end, so the result is marked as approximate and rounded to the nearest cent, with a more precise figure below it.
A negative principal, a negative rate, a negative time, or an n that is not a whole number from 1 to 525600 is rejected. Those values sit outside this classroom formula.
Frequently Asked Questions
What is the formula for compound interest?
The compound interest formula is A = P(1 + r/n)^(nt). P is the principal, r is the annual rate as a decimal, n is the number of compounds per year, and t is the time in years. A is the principal plus the interest. For 1000 dollars at 5% compounded monthly for 1 year, n = 12 and A is about $1,051.16.
How do you calculate compound interest monthly?
Use n = 12 in A = P(1 + r/n)^(nt). A 5% annual rate has r = 0.05, so the monthly piece inside the formula is 0.05/12. On a principal of 1000 for 1 year, A = 1000(1 + 0.05/12)^(12×1). Rounded to the nearest cent, that is about $1,051.16, and the interest is about $51.16.
What is 1000 at 5% compounded annually for 1 year?
Compounded annually means n = 1, so A = 1000(1 + 0.05/1)^(1×1) = 1000 × 1.05 = 1050. The amount is exactly $1,050.00 and the interest is exactly $50.00.
What is the formula for interest compounded continuously?
The compounded continuously formula is A = Pe^(rt). P is the principal, e is the base of the natural log, r is the annual rate as a decimal, and t is the time in years. There is no n. For 1000 at 5% for 1 year, A = 1000e^(0.05×1), about $1,051.27.
What happens when the rate is 0 or the principal is negative?
A rate of 0% gives A = P and interest of 0. A time of 0 years does too. A negative principal is not valid here, and neither is a negative rate, a negative time, or fewer than 1 compound per year.