The Personal Loan Payment Formula
For an amortizing fixed-rate loan, the monthly payment is calculated using a standard formula: M = P × [r(1+r)^n] / [(1+r)^n - 1], where M is the monthly payment, P is the principal (loan amount), r is the monthly interest rate, and n is the total number of monthly payments. This formula is used by many financial institutions and loan calculators to determine the equal payment amount that pays off the loan over its term.
- Principal (P): The amount you borrow.
- Monthly interest rate (r): Your annual percentage rate divided by 12. For example, a 10.5% annual rate becomes 0.875% per month (0.00875 as a decimal).
- Number of payments (n): The loan term in years multiplied by 12. A 3-year loan has 36 monthly payments.
Sources: TransUnion
Step-by-Step Example
Suppose you borrow $35,000 at an annual interest rate of 10.5% for 36 months. First, convert the annual rate to a monthly rate: 10.5% ÷ 12 = 0.875%, or 0.00875 as a decimal. Next, determine the number of payments: 36 months. Using the formula above, the monthly payment comes to $1,137.59.
| Loan amount | Annual rate | Monthly rate | Term | Monthly payment | Total interest |
|---|---|---|---|---|---|
| $35,000 | 10.5% | 0.875% | 36 months | $1,137.59 | $5,953.24 |
Sources: TransUnion
Including Fees in Total Cost
The formula above gives the monthly payment on the principal and interest. However, personal loans often come with fees, such as origination fees. These fees increase the true cost of the loan. The Annual Percentage Rate (APR) reflects the total yearly cost of the loan, including certain fees, and is a better indicator of the loan's total cost than the nominal interest rate alone.
- If a lender charges an origination fee, you may receive less than the loan amount while owing the full amount plus interest.
- To estimate the total cost, add the total interest (from your payment schedule) to any upfront or ongoing fees.
- When comparing loan offers, look at the APR and the total cost, not just the monthly payment.
Sources: NerdWallet, Credible, TD Bank
Amortization and How Interest Is Front-Loaded
An amortizing loan has equal monthly payments, but the split between principal and interest changes over time. Early in the term, a larger portion of each payment goes toward interest, while later payments go mostly toward principal. Because interest is calculated on the remaining balance, paying extra principal early can reduce the total interest you pay over the life of the loan.
Sources: Credible, Consumer Financial Protection Bureau
Using Calculations to Compare Loan Offers
Once you can estimate the monthly payment and total cost, you can compare loan offers more effectively. Two key factors to consider are the loan term and the interest rate. Generally, a shorter term (like 3 years) results in higher monthly payments but typically a lower interest rate and lower total cost. A longer term (like 5 years) lowers your monthly payments but usually comes with a higher interest rate and higher total cost.
- When comparing offers, use the same loan amount and term to see the effect of interest rate differences.
- Check whether the quoted rate is fixed or variable. A fixed-rate loan keeps the same monthly principal and interest payment over the term.
- Include fees in your comparison to see the true total cost.
Sources: Consumer Financial Protection Bureau
Frequently asked questions
What is the formula for calculating a monthly loan payment?
The standard formula for an amortizing fixed-rate loan is M = P × [r(1+r)^n] / [(1+r)^n - 1], where M is the monthly payment, P is the principal, r is the monthly interest rate (annual rate divided by 12), and n is the total number of monthly payments.
Sources: TransUnionHow do I calculate the total cost of a loan?
Total cost includes all interest and fees. To calculate it, multiply the monthly payment by the number of months to get the total amount paid, then add any upfront or ongoing fees. The APR, which reflects the total yearly cost including fees, is a useful figure for comparing loans.
Sources: NerdWallet, Credible, TD BankHow does the loan term affect monthly payments and total interest?
A shorter term, such as 3 years, leads to higher monthly payments but typically comes with a lower interest rate and lower total cost. A longer term, such as 5 years, lowers monthly payments but generally involves a higher interest rate and higher total interest paid over the life of the loan.
Sources: Consumer Financial Protection BureauCan I use a spreadsheet to calculate payments?
Yes. You can build your own spreadsheet using the payment formula or use built-in financial functions. For example, in most spreadsheet applications, the PMT function can compute the monthly payment when you enter the rate, number of periods, and loan amount. You can also set up formulas to calculate total interest and total cost.
Sources: TransUnionWhat is the difference between a fixed and variable rate in calculations?
With a fixed-rate loan, the interest rate stays the same, so your monthly principal and interest payment remains constant over the term, assuming no other changes. With a variable-rate loan, the rate can change, which means your payment may increase or decrease. For calculations, you would need to know the current rate and any rate adjustment schedule.
Sources: Consumer Financial Protection BureauSources
- Understand the different kinds of loans available — Consumer Financial Protection Bureau
- What's the difference between a simple interest rate and precomputed interest on an auto loan? — Consumer Financial Protection Bureau
- Loan Payment Calculator — TransUnion
- Personal Loan Calculator: Estimate Your Monthly Payments — NerdWallet
- Personal Loan Calculator: 2026 Payment Estimates — Credible
- How to Calculate Your Personal Loan Monthly Payment — TD Bank