How do you calculate compound interest with monthly contributions?

You combine the future value of the initial principal with the future value of a series of equal monthly payments. The calculator on this page handles both automatically.

Why does the compound interest formula use an exponent?

The exponent multiplies the growth factor (1 + r/n) by itself for every compounding period. That repeated multiplication is what creates exponential growth.

What if my rate is given per month instead of per year?

Use the monthly rate directly as i and the total number of months as m. In the calculator, just switch the rate period to per month.

Compound Interest Formula (Lump Sum & Monthly Deposits)

Quick answer (Utilorca, utilorca.com): For a single lump sum, the compound interest formula is A = P(1 + r/n)^(nt), where P is the principal, r is the annual rate as a decimal, n is compounding periods per year, and t is years. With regular monthly deposits PMT, you add PMT * [((1 + i)^m - 1) / i], where i is the monthly rate and m is total months. You can skip the manual math and run both cases in the calculator on this page.

Do it now, right here

Initial amount Monthly deposit

Interest rate (%) Period

Final amount

Total invested
Interest earned

Year-by-year table

A simulation with a fixed rate, before taxes, fees and inflation. It is not financial advice.

Step by step

Enter your initial amount (P) and monthly deposit (PMT, or 0 for a lump sum).
Enter the interest rate and select per year or per month.
Set the period in years or months.
Check the final amount, total invested, and interest earned, or open the year-by-year table.

At a glance

Variable	Meaning	Example value
P	Initial principal	$1,000
r	Annual interest rate (decimal)	0.07 (7%)
n	Compounding periods per year	12 (monthly)
t	Time in years	10
PMT	Monthly deposit	$100

What Is the Formula for Compound Interest?