Most installment loans — personal loans, student loans, auto loans, home-improvement loans — share the same structure: a fixed amount borrowed, a fixed rate and equal monthly payments that pay the balance down to zero. That structure links four numbers together, and if you know any three of them you can find the fourth. This loan calculator solves for whichever one you are missing and lays out the month-by-month schedule behind it.
How to use the loan calculator
- Pick what you want to solve for: the monthly payment, the loan amount you can borrow, the term needed to repay, or the interest rate.
- Fill in the three remaining values. The term can be entered in months or years.
- Optionally add the first payment date to see the payoff date and a dated schedule.
- Read the answer on the tape, then check the chart of the shrinking balance and the yearly and monthly amortization tables.
Loan formulas
All four modes come from one equation that sets the loan amount equal to the present value of the payments:
Rearranged for the payment, it becomes the familiar annuity formula:
And solved for the number of payments:
Here P is the amount borrowed, M the monthly payment, r the annual rate divided by 12 and n the number of months. The rate cannot be isolated algebraically, so the calculator finds it with a numerical root-finding method that converges to well under a millionth of a percent.
Worked example
You borrow $25,000 at 7% for 60 months.
Monthly rate: r = 0.07 ÷ 12 = 0.0058333
Growth factor: (1 + r)60 = 1.417625
Payment: 25,000 × 0.0058333 × 1.417625 ÷ 0.417625 = $495.03
Total paid: $29,701.80, of which $4,701.80 is interest.
Run it the other way and the numbers hold: a $400 monthly budget at 7% for 60 months supports a loan of about $20,200.80, and paying $600 a month on the original $25,000 clears it in 48 payments (47.88, rounded up) with $3,725.81 of interest.
How the term changes the cost
For the same $25,000 at 7%, here is the trade-off between the payment and the total interest:
| Term | Monthly payment | Total interest |
|---|---|---|
| 36 months | $771.93 | $2,789.39 |
| 48 months | $598.66 | $3,735.49 |
| 60 months | $495.03 | $4,701.80 |
| 72 months | $426.23 | $5,688.21 |
| 84 months | $377.32 | $6,694.63 |
Each extra year lowers the payment by a shrinking amount while the interest keeps climbing by roughly $1,000. For a grid across several rates at once, use the loan payment table.
Reading the amortization schedule
Interest each month is the remaining balance times the monthly rate, and whatever is left of the payment reduces the principal. Early payments are therefore interest-heavy: in the example, the first payment is $145.83 interest and $349.20 principal, while the last is under $3 of interest. Extra payments made early save the most because they remove principal before it accrues months of interest — the amortization calculator models them.
When this calculator fits
It assumes a fixed rate, monthly payments and no balloon. For weekly or bi-weekly payments, a different compounding frequency or a balloon payment, use the advanced loan calculator. If you know your budget rather than the loan amount, the loan affordability calculator adds a debt-to-income check.
Results are estimates for planning. Lenders may round payments, charge fees or use daily interest, so your loan agreement and Truth in Lending disclosure are the authoritative figures.
Frequently asked questions
How is a monthly loan payment calculated?
The payment on a fixed-rate installment loan uses the annuity formula M = P × 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. A $25,000 loan at 7% for 60 months works out to $495.03 a month.
Can I find the interest rate if I only know the payment?
Yes. Choose Rate in the Solve for control and enter the amount, term and payment. There is no algebraic formula for the rate, so the calculator searches numerically for the monthly rate that makes the payments repay the loan exactly, then multiplies it by 12 to give the APR.
Why is the last payment smaller when I solve for the term?
A fixed payment rarely divides the balance into a whole number of months. The calculator rounds up to the next whole month, and the final payment only needs to cover what is left, so it is usually smaller than the others.
Does a longer term save money?
A longer term lowers the monthly payment but raises the total interest, because the balance stays outstanding for longer. Stretching a $25,000, 7% loan from 36 to 72 months cuts the payment from $771.93 to $426.23 but roughly doubles the interest.
Are fees included in the payment?
No. The calculator uses the amount borrowed and the stated rate. If a lender charges an origination fee, use the APR calculator to see how the fee raises the true annual cost of the loan.