Your monthly loan payment is M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the amount you borrow, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. For example, a $20,000 loan at 6% APR over 5 years costs $386.66 per month, with $3,199.36 in total interest. This guide explains each part of the formula, works through that example step by step, shows how amortization splits each payment, and compares loan terms with verified totals.
If you want the answer for your own numbers without doing the arithmetic, use the free loan calculator — enter the loan amount, rate and term and it computes your monthly payment instantly.
What Is the Loan Payment Formula?
Most personal loans, auto loans and student loans are amortizing loans: you pay the same amount every month, and each payment covers that month’s interest plus a slice of the principal. The formula finds the fixed monthly payment that exactly pays off the loan, with interest, over the term.
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
- P — principal: the amount you borrow. If you finance a $24,000 car with $4,000 down, P is $20,000.
- r — monthly interest rate: the annual percentage rate (APR) divided by 12. At 6% APR, r = 0.06 ÷ 12 = 0.005.
- n — number of payments: years × 12. A 5-year loan has n = 60 payments; a 3-year loan has n = 36.
- M — monthly payment: the fixed amount you pay each month, covering both interest and principal.
The formula looks intimidating, but each piece is simple: (1 + r)^n is just the compounding factor over the whole loan, and the formula balances it so the loan reaches exactly zero at the final payment.
How Do You Calculate a Loan Payment? Step-by-Step
Worked example: $20,000 at 6% APR over 5 years.
- Monthly rate: r = 0.06 ÷ 12 = 0.005.
- Number of payments: n = 5 × 12 = 60.
- Compounding factor: (1 + 0.005)^60 = 1.3489.
- Numerator: P × r × factor = 20,000 × 0.005 × 1.3489 = 134.89 (approximately, before rounding).
- Denominator: factor − 1 = 1.3489 − 1 = 0.3489.
- Divide: 134.89 ÷ 0.3489 = $386.66 per month.
Over 60 payments that totals 60 × $386.66 = $23,199.36, of which $3,199.36 is interest. In other words, borrowing $20,000 on these terms costs you about 16% on top of the amount borrowed — and the rate and term you choose move that cost a lot, as the comparisons below show.
Second example: $15,000 at 8% APR over 3 years. Here r = 0.08 ÷ 12 = 0.0066667 and n = 36, which gives $470.05 per month, or $16,921.64 over the life of the loan — $1,921.64 of it interest. The monthly payment is higher than the first example even though the loan is smaller, because the term is shorter; the total interest is lower for the same reason.
How Does Amortization Work on a Loan?
Amortization is the schedule by which your fixed payment is split between interest and principal over time. Because interest is charged on the remaining balance, early payments are more heavily weighted toward interest and later payments mostly pay down principal — even though the total payment never changes.
On the $20,000, 6% example, the first payment breaks down like this: interest = $20,000 × 0.005 = $100.00, so principal = $386.66 − $100.00 = $286.66. After that payment the balance is $19,713.34. After 12 payments the balance is about $16,463.94 — you paid about $4,639.87 in the first year, and about $3,536.06 of it went to principal. The balance falls slowly at first, then faster every year as the interest portion shrinks.
Extra payments attack the principal directly. On this same loan, paying an extra $100 a month ($486.66 total) pays the loan off in about 47 months instead of 60 — 13 months early — and saves about $755 in interest.
How Does the Loan Term Change Your Payment and Total Cost?
The term is the biggest lever you control: a longer term lowers the monthly payment but raises the total interest, because you are renting the money for longer. Using the same $20,000 loan at 6% APR:
| 3-year | 5-year | 7-year | |
|---|---|---|---|
| Monthly payment | $608.44 | $386.66 | $292.17 |
| Number of payments | 36 | 60 | 84 |
| Total paid | $21,903.79 | $23,199.36 | $24,542.37 |
| Total interest | $1,903.79 | $3,199.36 | $4,542.37 |
Stretching the loan from 3 years to 7 years cuts the payment by $316.27 a month, but costs an extra $2,638.58 in interest. Stretching from 5 years to 7 years saves only $94.49 a month while adding $1,343.01 in interest — the longer the term, the less monthly relief each extra year buys. A practical rule: choose the shortest term whose payment still fits your budget comfortably.
What Else Affects the Cost of a Loan?
The formula uses the interest rate, but the APR and the loan’s fees decide what you really pay:
- Interest rate vs APR: the rate sets your payment; the APR also folds in lender fees such as origination charges, so APR is the better number for comparing offers.
- Origination and other fees: some lenders take 1%–8% of a personal loan off the top or add it to the balance — either way it raises your true cost beyond the payment figure.
- Prepayment penalties: uncommon on personal and auto loans, but check the fine print — a penalty can wipe out the savings from paying extra each month.
- Fixed vs variable rate: everything above assumes a fixed rate, so the payment never changes. A variable-rate loan can start lower but its payment can rise if market rates climb.
One loan works differently and is worth a quick note: a home loan uses exactly the same amortization formula, but the payment you actually hand over each month usually also includes property taxes and insurance. If you are comparing a home purchase, use the free mortgage calculator, which adds those costs on top of the principal and interest worked out here.
That is the full picture for a standard loan: the formula sets the fixed payment, amortization explains where each payment goes, the term sets the total interest, and the APR reveals the true cost. Run your own figures through the free loan calculator before you sign anything, so you know the payment — and the total cost — you are actually agreeing to.
Frequently Asked Questions
What is the formula for calculating a loan payment?
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), where P is the amount borrowed, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. It gives the fixed monthly payment for an amortizing loan at a fixed rate.
How much is a $20,000 loan at 6% over 5 years?
$386.66 per month. With r = 0.06 ÷ 12 = 0.005 and n = 60, the compounding factor (1 + r)^n is 1.3489, giving 20,000 × 0.005 × 1.3489 ÷ 0.3489 = $386.66. Total paid over 5 years is $23,199.36, of which $3,199.36 is interest.
How is loan interest calculated each month?
Each month’s interest is the current balance multiplied by the monthly rate (annual rate ÷ 12). On a $20,000 loan at 6%, the first month’s interest is $20,000 × 0.005 = $100.00, so $286.66 of the $386.66 payment reduces the balance. As the balance falls, the interest portion shrinks and the principal portion grows.
Is a shorter or longer loan term better?
A shorter term costs more per month but far less overall. On $20,000 at 6%, a 3-year loan costs $608.44 a month with $1,903.79 total interest, while a 7-year loan costs $292.17 a month but $4,542.37 in interest. Choose the shortest term whose payment fits your budget comfortably.
Does paying extra each month really save money?
Yes, because extra payments reduce the principal directly, so less interest is charged every month after. Adding $100 a month to a $20,000 loan at 6% over 5 years pays it off in about 47 months instead of 60 and saves about $755 in interest. Check first that your loan has no prepayment penalty.
What is the difference between the interest rate and APR?
The interest rate sets your monthly payment. The APR includes the rate plus lender fees such as origination charges, expressed as a yearly rate, so it reflects the loan’s true cost more completely. When comparing offers, compare APRs, not just rates or monthly payments.
