Every fixed-rate installment loan -- personal, debt consolidation, equipment, a loan from a relative -- uses the same amortization formula. Master it once and you can price any loan: M = P x [ r(1+r)^n ] / [ (1+r)^n - 1 ], where P is the amount borrowed, r is the monthly rate, and n is the number of payments.
This guide walks through the formula by hand, the one-line Excel version, and how to read whether your quoted rate is even good. You can check every result against the Loan Calculator.
The three inputs that set every payment
- P -- the amount financed. What you actually borrow. If a fee is added to the loan, include it here.
- r -- the monthly rate. Take the annual rate and divide by 12. A 9% APR becomes 0.09 / 12 = 0.0075.
- n -- the number of payments. Years times 12. A 4-year loan is 48.
A worked example by hand
Borrow $12,000 at 9% APR over 4 years (48 months).
- Monthly rate: r = 0.09 / 12 = 0.0075
- Growth factor: (1 + 0.0075)^48 = 1.431405
- Top: 0.0075 x 1.431405 = 0.01073554
- Bottom: 1.431405 - 1 = 0.431405
- Payment: $12,000 x (0.01073554 / 0.431405) = $298.62
Over 48 months you repay $14,333.78, so total interest is about $2,333.78. That matches the calculator to the penny.
The Excel / Google Sheets one-liner
You don't need the longhand formula in a spreadsheet. Use the built-in PMT function:
=PMT(0.09/12, 48, -12000)
This returns 298.62. The rate is divided by 12, the term is in months, and the loan amount is entered as a negative so the payment comes back positive. Change any input and the payment updates instantly -- the same thing the Loan Calculator does, with an amortization schedule on top.
This works for ANY loan type
The formula doesn't care what the loan is for. The only differences between an auto loan, a personal loan, and a home equity loan are the typical rate and the typical term -- the math is identical. That's why one general calculator can price them all. For loans where the amount financed has extra moving parts (taxes, trade-ins, points), a specialized tool just helps you find P; the payment still comes from this formula. Examples: the Auto Loan Calculator, the Mortgage Calculator, and the Business Loan Calculator all run the same engine.
How the term changes everything
A longer term lowers the monthly payment but raises total interest. Here's the same $12,000 at 9% across common 2-to-7-year terms:
| Term | Monthly payment | Total interest |
|---|---|---|
| 2 years (24 mo) | $548.22 | $1,157 |
| 3 years (36 mo) | $381.60 | $1,737 |
| 4 years (48 mo) | $298.62 | $2,334 |
| 5 years (60 mo) | $249.10 | $2,946 |
| 7 years (84 mo) | $193.07 | $4,218 |
Going from 2 to 7 years cuts the payment by more than half but nearly quadruples the interest. Pick the shortest term whose payment fits your budget.
Is your quoted rate any good?
Unsecured personal loan rates are priced mostly off your credit score: stronger credit gets lower rates because the lender's risk is lower. Rates move over time, so treat these as illustrative tiers, not current quotes. Here's how the same $10,000 over 36 months behaves at different rates so you can feel the cost of each tier:
| Rate (illustrative) | Monthly payment | Total interest |
|---|---|---|
| 8% | $313.36 | $1,281 |
| 13% | $336.94 | $2,130 |
| 18% | $361.52 | $3,015 |
| 25% | $397.60 | $4,314 |
| 32% | $435.54 | $5,680 |
The takeaway: a few points of rate is real money. If your quote sits in a high tier, improving your credit before borrowing -- or putting up collateral for a secured loan -- can move you down a row and save hundreds to thousands.
Compare the rate, not the nominal number
When you shop, compare loans by APR, which folds in fees like origination charges, not the headline nominal rate. Two loans can show the same rate but very different APRs once fees are added. The U.S. CFPB explains the rate-vs-APR difference in plain terms.
Once you know your payment, sanity-check that it fits your income with the Loan Affordability Calculator, and if you're juggling multiple debts, plan the order with the Debt Payoff Calculator.
Try it yourself
Run your own numbers in the free Loan Calculator — instant, private, no sign-up.
Open the Loan Calculator →Frequently asked questions
- What is the formula to calculate a loan payment?
- The monthly payment formula is M = P x [ r(1+r)^n ] / [ (1+r)^n - 1 ], where P is the amount borrowed, r is the annual rate divided by 12, and n is the number of monthly payments. For $12,000 at 9% over 48 months, that gives about $298.62 per month.
- How do I calculate a loan payment in Excel?
- Use the PMT function: =PMT(rate/12, months, -loan_amount). For example, =PMT(0.09/12, 48, -12000) returns 298.62. Divide the annual rate by 12, put the term in months, and enter the loan amount as a negative so the payment is positive.
- Does the same formula work for any type of loan?
- Yes. Auto loans, personal loans, debt consolidation loans, business loans, and home equity loans all use the identical amortization formula. The only differences are the typical rate and term, which is why one general loan calculator can price any fixed-rate loan.
- How much does the loan term change what I pay?
- A longer term lowers the monthly payment but raises total interest. On $12,000 at 9%, a 2-year loan costs about $548/month and $1,157 in interest, while a 7-year loan costs about $193/month but $4,218 in interest -- nearly four times as much. Choose the shortest term whose payment fits your budget.
- What rate should I expect on a personal loan?
- Unsecured personal loan rates are priced mainly by your credit score -- stronger credit earns lower rates. Rates change over time, so compare quotes by APR rather than relying on a fixed benchmark. On $10,000 over 36 months, every five points of rate adds roughly $850 or more in total interest.
- Should I compare loans by interest rate or APR?
- Compare by APR. The APR includes fees like origination charges, so it reflects your true cost, while the nominal interest rate does not. Two loans with the same stated rate can have very different APRs once fees are added in.
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