How to Calculate an Interest Rate (Formula and Excel)

Knowing the interest rate is the only way to compare a loan, a financing offer or an investment fairly. Often, though, you are given everything except the rate: the payment, the price, the amount you’ll get back. This guide shows how to figure out the interest rate in three common situations, with a formula, a worked example and the matching Excel function for each.

Which method do you need?

What you know	Method	Excel function
Interest paid, principal and time	Simple interest formula	Direct formula
Starting value, ending value and years	Compound growth rate	RRI
Loan amount, payment and number of payments	Solve the payment equation	RATE

The interest rate calculator handles the loan and growth cases in your browser, without Excel.

Method 1: simple interest

When interest is charged only on the original principal, the formula rearranges neatly:

interest = principal × rate × time
rate = interest ÷ (principal × time)

Example: you paid $450 of interest on a $5,000 loan over 18 months (1.5 years). Rate = 450 ÷ (5,000 × 1.5) = 6% a year.

Use this for short-term loans, some personal loans between friends and family, and Treasury bills. The simple interest calculator works in the other direction, from a rate to the interest.

Method 2: growth rate from two values

If money grew from one amount to another over several years with compounding, the yearly rate is the compound annual growth rate (CAGR):

rate = (ending value ÷ starting value)^(1 ÷ years) − 1

Example: an investment grew from $10,000 to $14,000 in 5 years. Rate = 1.4^(1/5) − 1 = 6.961% a year.

In Excel: =RRI(5, 10000, 14000) returns 0.0696, which is 6.96%.

Method 3: interest rate on a loan with payments

For a loan with equal monthly payments, the rate is hidden inside the amortization formula:

payment = amount × r ÷ (1 − (1 + r)^−n)

You can’t rearrange this to isolate r, so the rate is found by trial and error. Financial calculators, Excel and our tools all do this automatically.

Worked example: a dealer financing offer

A dealer offers $20,000 of financing at $400 a month for 60 months.

1. Total paid: 400 × 60 = $24,000, so the interest is $4,000.
2. The monthly rate that makes 60 payments of $400 worth exactly $20,000 today is 0.618%.
3. The annual rate is 0.618% × 12 = 7.42%.
4. With monthly compounding, the effective annual rate is (1.00618)¹² − 1 = 7.678%.

How to calculate an interest rate in Excel

RATE: interest rate on a loan or annuity

=RATE(nper, pmt, pv, [fv], [type], [guess])

• nper: number of payments (60)
• pmt: the payment, negative because you pay it (−400)
• pv: the amount you receive (20000)
• fv: optional, the balance left at the end (usually 0)
• type: 0 for payments at the end of each period, 1 for the start

=RATE(60,-400,20000) returns 0.618%, the monthly rate. Multiply by 12 for the annual rate: *=RATE(60,-400,20000)12 gives 7.42%.

RRI: growth rate between two values

=RRI(years, start, end), for example =RRI(5,10000,14000) = 6.96%.

EFFECT and NOMINAL: switching between rates

• =EFFECT(7.42%, 12) converts a nominal annual rate compounded monthly into the effective annual rate, 7.678%.
• =NOMINAL(7.678%, 12) goes the other way.

If RATE returns #NUM!, check the signs (the payment and present value must have opposite signs) or add a guess such as 0.01 as the last argument.

Monthly, daily and annual interest rates

Rates are quoted per year, but interest is often charged per month or per day:

• Monthly rate: annual rate ÷ 12. A 7.42% loan charges 0.618% a month.
• Daily rate: annual rate ÷ 365 (some lenders use 360). A 24.99% credit card charges about 0.0685% a day, so a $5,000 balance builds roughly $102.70 of interest over 30 days.
• Effective annual rate: (1 + periodic rate)^(periods per year) − 1. Compounding makes this higher than the quoted annual rate.

When someone quotes “1.5% a month”, convert it before comparing. As a nominal rate, that is 18% a year. With compounding, it is 19.56%.

Finding the rate on a savings account or CD

Banks advertise savings accounts and CDs by APY, which already includes compounding. To find the underlying interest rate, reverse the compounding:

nominal rate = ((1 + APY)^(1 ÷ periods per year) − 1) × periods per year

An account advertising 4.5% APY with monthly compounding has a nominal rate of ((1.045)^(1/12) − 1) × 12 = 4.410%. If you already know the result, the growth method works too: a $10,000 one-year CD that pays back $10,460 earned exactly 4.6% for the year. When you compare a savings rate with a loan rate, convert both to the same basis first, APY with APY or nominal with nominal.

Nominal vs. real interest rates

The rates above are nominal: they ignore inflation. The real interest rate shows how much your purchasing power actually grows:

real rate = (1 + nominal rate) ÷ (1 + inflation) − 1

A savings account paying 7% while inflation runs at 3% has a real rate of 1.07 ÷ 1.03 − 1 = 3.883%. The quick approximation, 7% − 3% = 4%, is close for low rates but drifts as rates rise. For a borrower, high inflation lowers the real cost of a fixed-rate loan. For a saver, it erodes returns.

The equilibrium interest rate (economics)

In a macroeconomics course, “how to calculate the equilibrium interest rate” means finding the rate where money demand equals money supply (or where savings equal investment).

Example: money demand is Md = 500 − 20r, where r is the interest rate in percent, and the central bank fixes the money supply at Ms = 300.

1. Set them equal: 500 − 20r = 300.
2. Solve: 20r = 200, so r = 10%.

If the central bank raises the money supply, the equilibrium rate falls, and if it shrinks the supply, the rate rises.

Common mistakes

• Mixing monthly and yearly rates. A rate per month must be multiplied by 12 (nominal) or compounded (effective) before you compare it with an annual rate.
• Ignoring fees. The rate from the payment alone ignores upfront fees. The APR calculator includes them.
• Using the purchase price instead of the amount borrowed. Subtract any down payment first.
• Wrong signs in Excel. RATE needs cash in and cash out to have opposite signs.
• Comparing rates with different compounding. A loan quoted at 12% compounded monthly costs more than one at 12% compounded yearly. Convert both to an effective annual rate before you decide.

For any other unknown, such as the payment, the term or the future value, use the finance calculator. To see how a rate turns into growth over time, use the compound interest calculator.

Frequently asked questions

How do I calculate an interest rate from a monthly payment?

You need the amount borrowed, the payment and the number of payments. In Excel, use =RATE(number of payments, −payment, amount)*12. For $20,000 repaid at $400 a month for 60 months, that gives 7.42% a year.

What is the formula for an interest rate?

For simple interest, rate = interest ÷ (principal × years). For growth over several years, rate = (ending value ÷ starting value)^(1 ÷ years) − 1. For a loan with level payments there is no closed formula, so the rate is found by trial and error, which is what RATE does.

How do I find the monthly interest rate?

Divide the annual rate by 12 for a nominal monthly rate. 7.42% a year is 0.618% a month. To go from a monthly rate to an effective yearly rate, use (1 + monthly rate)^12 − 1.

Why does Excel's RATE return

Usually because the payment and the present value have the same sign. Enter money you receive as positive and money you pay as negative, for example =RATE(60,-400,20000). You can also give Excel a starting guess as the sixth argument.

What is the equilibrium interest rate?

In economics, it is the interest rate at which the amount of money people want to hold equals the money supply, or at which savings equal investment. It is found by setting the demand and supply equations equal and solving for the rate.