Interest Rate Calculator
Find the annual interest rate that turns a starting amount into an ending amount over a number of years.
Back-solve annual growth rate from principal, final amount, and years.
How to use this calculator
Find the rate from a start and end amount
If you know how much money you started with, how much you ended with, and how many years passed, this calculator finds the annual interest rate that connects them. It assumes interest compounded once a year, with no deposits or withdrawals in between.
It answers questions like “what rate turns $10,000 into $15,000 in 5 years?” The answer is 8.45% a year. Dividing the $5,000 gain by 5 years suggests 10%, which overstates the rate because each year’s interest also earns interest.
Where this is useful
Use it to check an offer quoted as a dollar amount, such as a bond, annuity, or savings product that promises a set payout on a set date. Converting that promise into an annual rate makes it easy to compare with a savings account, a CD, or the rate on your debt.
It also works backward from results you already have. If an account grew from $10,000 to $12,000 over 3 years, it earned 6.27% a year. If the ending amount is lower than the start, the rate is negative: $10,000 falling to $9,000 over 3 years is −3.45% a year.
Limits of a single rate
The result is an average. Real accounts rarely grow at the same rate every year, and investment returns can swing widely. Two investments with the same starting and ending values get the same rate here, even if one was far more volatile along the way.
Deposits and withdrawals also change the picture. If you added money along the way, the ending balance includes those deposits, so this formula would overstate the rate. For a series of deposits you need an internal rate of return (IRR) calculation instead.
You can also review Compound Interest Calculator and Investment Growth Calculator to compare scenarios.
Formula
- Annual rate = (ending amount ÷ starting amount)^(1 ÷ years) − 1
- Example: (15,000 ÷ 10,000)^(1 ÷ 5) − 1 = 0.0845, or 8.45%
Example: $10,000 grows to $15,000 in 5 years
- Growth multiple: $15,000 ÷ $10,000 = 1.5.
- Take the 5th root: 1.5^(1/5) ≈ 1.0845.
- Subtract 1: the annual rate is 8.45%.
- Check: $10,000 × 1.0845^5 ≈ $15,000.
Annual rate for common outcomes
Starting from $10,000, compounded once a year.
| Final amount | Years | Annual rate |
|---|---|---|
| $11,000 | 2 years | 4.88% |
| $12,000 | 3 years | 6.27% |
| $15,000 | 5 years | 8.45% |
| $20,000 | 5 years | 14.87% |
| $20,000 | 10 years | 7.18% |
| $30,000 | 15 years | 7.6% |
| $9,000 | 3 years | -3.45% |
Frequently asked questions
What interest rate doubles money in 10 years?
About 7.18% a year, compounded annually. The Rule of 72 gives a quick estimate of 7.2% (72 ÷ 10).
Is this the same as CAGR?
Yes. The compound annual growth rate uses the same formula. “Interest rate” is the usual term for savings and loans, while CAGR is common for investments and business growth.
Does compounding frequency change the result?
This calculator reports an annually compounded rate, which equals the effective annual rate or APY. A nominal rate compounded monthly would be slightly lower for the same growth: 8.45% compounded annually equals about 8.14% compounded monthly.
Can the rate be negative?
Yes. If the ending amount is lower than the starting amount, the result is a negative annual rate, showing how fast the value shrank on average.
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