The formula, in one paragraph
Start with the loan amount, the APR and the term in months. Divide the APR by 12 to get the monthly rate, raise one plus that rate to the power of the months, and the payment is the loan times the monthly rate times that growth factor, divided by the growth factor minus one. Six steps, all arithmetic — the worked example below shows every one.
Step 1: Find the monthly rate
The APR is an annual rate, but the payment is monthly, so the first step is to divide by 12. At 10.5% a year, the monthly rate is 10.5% divided by 12, which is 0.875% a month, or 0.00875 as a decimal. This is the rate that prices every payment: the first month’s interest is the loan times this rate, which is $15,000 times 0.00875, or $131.25.
Step 2: Count the payments
The number of payments is the term in months: 48 months means 48 payments. If the term is quoted in years, multiply by 12 first. The count matters twice: it sets the growth factor in step 3 and the total paid in step 5.
Step 3: Raise one plus the rate to the power of the payments
The growth factor is one plus the monthly rate, raised to the power of the number of payments: (1 + 0.00875) to the power of 48, which is 1.51918. A longer term makes it bigger — at 72 months it is 1.87247 — and a higher rate makes it bigger faster.
Step 4: Work out the monthly payment
The payment is the loan times the monthly rate times the growth factor, divided by the growth factor minus one:
At the example numbers, that is $15,000 times 0.00875 times 1.51918, divided by 1.51918 minus 1 — $131.25 times 1.51918 divided by 0.51918 — which is $384.05 a month. The division by the growth factor minus one is what spreads the loan evenly across the term.
Step 5: Work out the total paid and the interest
The total paid is the payment times the number of payments: $384.05 times 48, which is $18,434.43. The interest is the total paid minus the loan: $18,434.43 minus $15,000, which is $3,434.43 — about 23% on top of the loan. Compare offers by interest, not by the monthly payment alone.
Step 6: Read the first payment
Every payment is the same $384.05, but what it is made of changes. The first month’s interest is the loan times the monthly rate — $15,000 times 0.00875, which is $131.25 — so the principal in the first payment is $384.05 minus $131.25, which is $252.80. The first year costs $1,424.66 of interest and the last year costs $251.75, because the balance shrinks with every payment.
Worked example: $15,000 loan, 10.5% APR, 48 months
Step 2: payments = 48.
Step 3: growth factor = (1 + 0.00875)^48 = 1.51918.
Step 4: payment = $15,000 × 0.00875 × 1.51918 ÷ (1.51918 − 1) = $384.05 a month.
Step 5: total paid = $384.05 × 48 = $18,434.43. Interest = $18,434.43 − $15,000 = $3,434.43.
Step 6: first payment = $131.25 interest + $252.80 principal. First-year interest $1,424.66; last-year interest $251.75.
Answer: $384.05 a month, $18,434.43 in all, $3,434.43 of interest.
What changes the payment most
The loan amount moves the payment in proportion: a $10,000 loan costs $256.03 a month and a $25,000 loan costs $640.08 a month, at the same rate and term. The rate moves the interest more than the payment: at 7% the payment is $359.19 a month and the interest is $2,241.30, while at 15% the payment is $417.46 a month and the interest is $5,038.14 — an 8-point gap is $58.27 a month but $2,796.84 of interest. The term moves them in opposite directions: 24 months costs $695.64 a month and $1,695.37 of interest, while 72 months costs $281.68 a month and $5,281.29 of interest.
Work backwards from your budget
When the budget is fixed, run the formula in reverse: the loan a payment affords is the payment times the growth factor minus one, divided by the monthly rate times the growth factor. At 10.5% for 48 months, $300 a month affords an $11,717.20 loan, $400 a month affords $15,622.94, and $500 a month affords $19,528.67. Start from the payment you can afford, not the loan you want.
Frequently asked questions
How do I calculate a personal loan payment by hand?
Divide the APR by 12 for the monthly rate, raise one plus that rate to the power of the months, and the payment is the loan times the monthly rate times that factor, divided by the factor minus one. On $15,000 at 10.5% for 48 months, the monthly rate is 0.875%, the factor is 1.51918, and the payment is $384.05 a month.
How much interest will I pay on a personal loan?
Multiply the payment by the months and subtract the loan. On $15,000 at 10.5% for 48 months, the total paid is $18,434.43 and the interest is $3,434.43. At 7% the interest is $2,241.30, and at 15% it is $5,038.14.
Why is most of my first payment interest?
Because the first month’s interest is the whole loan times the monthly rate: $15,000 times 0.875% is $131.25, about a third of the $384.05 payment. The first year costs $1,424.66 of interest and the last year costs $251.75, because the balance shrinks with every payment.
Does a longer term always cost more?
Yes, in interest — and less, in monthly payment. A 24-month term costs $1,695.37 of interest at $695.64 a month, and a 72-month term costs $5,281.29 of interest at $281.68 a month. Pick the shortest term whose payment fits your budget.
How much can I borrow with a $400 monthly payment?
$15,622.94 at 10.5% for 48 months. A $300 a month payment affords $11,717.20, and $500 a month affords $19,528.67, at the same rate and term.
Try it: run your own numbers through the free personal loan calculator — loan amount, APR and term, with the payment, total and interest broken out.