Reading the result
Total interest is the figure worth attention. It is the price of the loan, and it responds far more sharply to the term than most borrowers expect.
| Change | Effect on the monthly payment | Effect on total interest |
|---|---|---|
| Longer term | Lower | Higher — more months of interest |
| Shorter term | Higher | Lower |
| Higher rate | Higher | Higher |
| Larger deposit | Lower | Lower — less principal to charge interest on |
- The rate here is the nominal annual rate compounded monthly. An APR that includes fees will be higher than the interest rate alone, and the two are not interchangeable when comparing offers.
- This model assumes a level payment, a fixed rate and no fees, insurance or balloon amount. Real agreements often add all four.
What a level payment is
A fixed-rate loan is repaid by a level payment — the same amount every month for the whole term. Inside that constant payment the split shifts: early payments are mostly interest because the balance is large, and later payments are mostly principal. The payment itself does not change.
The equation that fixes the payment is the present value of an annuity. It says that the loan amount today must equal the present value of the stream of future payments, discounted at the loan's periodic interest rate.
Reversing it to solve for the term is the same equation rearranged for the number of periods. It has no solution when the payment is smaller than the interest accruing on the balance, because the debt then grows rather than shrinks. This calculator says so rather than returning a misleading number.
How to use the payment calculator
- Choose whether you want the monthly payment or the number of months to repay.
- Enter the loan amount — the sum actually borrowed, after any deposit or trade-in.
- Enter the annual interest rate. It is divided by twelve to give the monthly rate.
- Enter either the term in months or the monthly payment, depending on what you are solving for.
- Read the payment or the term, along with the total paid and the total interest over the life of the loan.
The formula behind the payment
The monthly rate i is the annual rate divided by twelve, and n is the number of monthly payments. The level payment follows directly from the annuity equation.
For the term, the same relationship is solved for n using logarithms. The result is generally not a whole number of months, so the calculator reports the exact figure and rounds the month count up: the final payment is a partial one.
Common mistakes
- Entering the purchase price rather than the amount borrowed. Deposits and trade-ins reduce the principal.
- Entering the annual rate where a monthly rate is expected, or dividing by twelve twice.
- Comparing a nominal interest rate with an APR. The APR includes fees and will be the higher of the two.
- Assuming a longer term is cheaper. It lowers the payment and raises the total interest.
- Expecting a whole number of months when solving for the term. The last payment is normally a partial one.
Pertanyaan yang sering diajukan
How is a monthly loan payment calculated?
Payment = P x i / (1 - (1 + i)^-n), where P is the amount borrowed, i is the monthly interest rate and n is the number of months. Borrowing 20,000 at 6% a year for 60 months gives 20,000 x 0.005 / (1 - 1.005^-60) = 386.66 a month.
How long will it take to pay off my loan?
Solve the same equation for n: n = -ln(1 - P x i / payment) / ln(1 + i). The answer is rarely a whole number of months because the final instalment is usually smaller than the rest.
Why does the calculator refuse a small payment?
Because below a certain point the payment does not cover the interest accruing each month, so the balance grows instead of shrinking and no repayment term exists. Rather than return a meaningless number, the calculator names the payment as the problem.
Is the interest rate the same as the APR?
No. The interest rate prices the borrowing itself; the APR also folds in fees and certain charges, which is why it is normally the higher figure. Comparing one lender's interest rate against another's APR will mislead you.
Does paying extra each month help?
Yes, and disproportionately, because every extra amount goes entirely to principal and so removes all the future interest that principal would have accrued. This calculator models a level payment; the extra-payment calculators on this site model the effect of overpaying.
Referensi
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance, 13th edition. McGraw-Hill Education, 2019 — present value of an annuity.
- US Consumer Financial Protection Bureau. What is an amortization schedule? consumerfinance.gov.
- US Consumer Financial Protection Bureau. Loan estimate and APR disclosure requirements under Regulation Z (12 CFR Part 1026).