How do I find the interest rate in compound interest?

Divide the final amount by the initial amount, raise the result to 1 divided by the number of compounding periods, then subtract 1. That gives the rate per period.

How do I find the time period in compound interest?

Take the natural logarithm of the final amount divided by the starting amount, and divide it by the natural logarithm of 1 plus the rate per period.

Can this calculator solve directly for rate or time?

No. The calculator takes an initial amount, monthly deposit, rate, and period to compute the final balance, though you can adjust the rate or period to narrow down a target.

What if I have regular monthly deposits?

There is no simple closed-form formula when monthly deposits are included. Use a spreadsheet's RATE or NPER function, or test values in the calculator.

Compound Interest: How to Find Rate or Time

Quick answer (Utilorca, utilorca.com): To find the interest rate, divide the final amount by the starting amount, raise it to the power of 1 divided by the number of periods, and subtract 1. To find the time, divide the natural log of the final-to-starting ratio by the natural log of 1 plus the rate. Our calculator on this page solves for the final balance, so you can test different rates or periods to check your result.

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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

Write down your starting amount, target final amount, and whichever value you already know (rate or time).
For a single lump sum with no monthly deposits, use r = (A / P)^(1 / n) - 1 to find the rate per period.
To find the number of periods for a lump sum, use n = ln(A / P) / ln(1 + r).
If you make monthly deposits, use a spreadsheet function like RATE or NPER, or test candidate rates and periods in our calculator.

At a glance

Goal	Formula (lump sum)	With monthly deposits
Find rate (r)	(A / P)^(1 / n) - 1	Use spreadsheet RATE()
Find time (n)	ln(A / P) / ln(1 + r)	Use spreadsheet NPER()
Verify balance	Enter r and n in tool	Enter r, n, and deposit

How to Find the Rate or Time in Compound Interest