How to calculate an interest rate
To calculate the interest rate from a start and an end balance, take the ratio, raise it to one over the number of years and subtract one: r = (FV ÷ PV)1/t − 1 for yearly compounding.[1] For other compounding, apply the same idea per period and multiply by the periods per year.
$10,000 to $15,000 in 6 years: 1.51/6 − 1 = 6.991% a year compounded yearly. Compounded monthly it is 6.777%, the nominal rate whose APY is the same 6.991%.[2][4] Once you add regular deposits there is no closed formula, so the calculator searches for the rate that fits.
Rate needed to grow money
The annual rate needed to multiply your money depends only on the multiple and the years:
| Time | Grow 1.5× | Double (2×) | Triple (3×) |
|---|---|---|---|
| 3 years | 14.47% | 25.99% | 44.22% |
| 5 years | 8.45% | 14.87% | 24.57% |
| 10 years | 4.14% | 7.18% | 11.61% |
| 20 years | 2.05% | 3.53% | 5.65% |
These are APYs. To double in 10 years takes about 7.2% a year, the same answer the rule of 72 gives. To see how much a given rate grows to instead, use the compound interest calculator; it can also solve for the rate with deposits and a target in "Rate needed" mode.
Interest rate on a loan from the payment
For a fixed-payment loan, the rate is the one that makes the standard amortization formula produce your payment. It has no algebraic solution, so lenders and spreadsheets (the RATE function) find it by trial.[3] A $20,000 loan over 60 months at different rates:
| Rate | Monthly payment | Total interest |
|---|---|---|
| 4% | $368.33 | $2,099.83 |
| 6% | $386.66 | $3,199.36 |
| 8% | $405.53 | $4,331.67 |
| 10% | $424.94 | $5,496.45 |
| 12% | $444.89 | $6,693.34 |
Paying $400 a month implies 7.42%, with $4,000.00 of interest over the loan. In a spreadsheet the same answer is =RATE(60, -400, 20000) * 12.
Rate vs APR on a loanThis calculator returns the interest rate built into the payment. A lender's APR also counts certain fees, so it can be higher than the rate found here.
Checking an advertised return
Working back to the rate is a quick way to check a claim. If an offer says $1,000 becomes $2,000 in 2 years, that is 41.4% a year, far beyond any savings account, CD or Treasury bill. Compare offers by APY: the APY calculator converts between a nominal rate and APY, and the CAGR calculator annualizes the growth of an investment.
Related calculators
- Compound interest calculatorDeposits, any compounding, inflation, goal seek, chart and CSV
- CAGR calculatorCompound annual growth rate between two values
- APY calculatorAPR to APY and back, for any compounding
- Interest calculatorInterest earned on a sum, simple or compound, every method side by side
Frequently asked questions
How do I calculate the interest rate?
With no deposits, divide the ending balance by the starting balance, raise the result to 1 ÷ years and subtract 1. With deposits or loan payments, solve numerically, as this calculator does.
What interest rate do I need to double my money?
About 7.2% a year for 10 years, 14.9% for 5 years and 3.5% for 20 years.
How do I find the interest rate on a loan from the monthly payment?
Enter the amount borrowed, the payment and the number of payments. A $20,000 loan at $400 a month for 60 months works out to 7.42% a year.
Is the result an APR or an APY?
For savings it is the nominal annual rate for the compounding you choose, with its APY shown beside it. For loans it is the annual rate compounded monthly; at 7.42% that is an effective 7.68% a year.