How the Loan Calculator Works
Every simple loan, such as a car loan, a personal loan or a student loan, is described by four numbers: the amount borrowed, the interest rate, the length of the loan and the monthly payment. If you know any three, you can work out the fourth. The Loan Calculator does that. Pick what you want to find, fill in the other numbers, and it does the rest.
The four things you can find
| You want to find | You enter |
|---|---|
| The monthly payment | Loan amount, interest rate, loan term |
| How much you can borrow | Interest rate, loan term, monthly payment |
| How long it takes to repay | Loan amount, interest rate, monthly payment |
| The interest rate | Loan amount, loan term, monthly payment |
The main formula
The yearly rate is divided by 12 to get the monthly rate r. With a loan of P and n monthly payments, the standard formula gives the payment:
payment = P x r x (1 + r)^n / ((1 + r)^n - 1)
If the rate is 0%, the payment is just P divided by n. The other three questions use the same relationship, turned around:
amount you can borrow = payment x (1 - (1 + r)^-n) / r months to repay = -ln(1 - P x r / payment) / ln(1 + r)
The interest rate has no simple formula, so the calculator finds it by trial. It tries rates, works out the payment each would give, and narrows in on the rate that matches your payment.
Month by month
After it has all four numbers, the calculator pays the loan off one month at a time. Each month, interest is charged on the balance you still owe. The rest of your payment reduces the loan. This gives the total interest, the total you repay, and what you still owe at the end of every year. If a payment is not a whole number of months, the last payment is smaller.
A worked example: find the payment
You borrow $20,000 at 7.5% for 4 years (48 months). The payment is $483.58. Over 48 payments you repay $23,211.75, so the interest is $3,211.75. This is what you still owe at the end of each year:
| Year | You pay | Interest | Goes to the loan | Still owed |
|---|---|---|---|---|
| 1 | $5,803 | $1,349 | $4,454 | $15,546 |
| 2 | $5,803 | $1,003 | $4,800 | $10,746 |
| 3 | $5,803 | $631 | $5,172 | $5,574 |
| 4 | $5,803 | $229 | $5,574 | $0 |
Chart: what you still owe
Start ████████████████████████████████████████ $20,000 Year 1 ███████████████████████████████ $15,546 Year 2 █████████████████████ $10,746 Year 3 ███████████ $5,574 Year 4 (paid off)
More examples
- How much can I borrow? You can pay $450 a month for 5 years at 6%. The most you can borrow is $23,276.50.
- How long will it take? You owe $20,000 at 7.5% and pay $600 a month. It takes 38 months, which is 3 years and 2 months.
- What is the rate? You borrowed $15,000 for 3 years and pay $523.34 a month. The interest rate is about 15.46%. This is useful for checking a loan offer that only states the payment.
Chart: the cost of a loan
Interest is the price of borrowing. In the first example, $3,211.75 of the $23,211.75 you repay is interest:
Loan ████████████████████████████████████ 86% Interest ██████ 14%
Tips
- A longer term lowers the payment but raises the total interest.
- Even a small increase in the payment can shorten the loan a lot. Try the "how long" question with a higher payment.
- If the payment does not cover the first month's interest, the loan would never shrink. The calculator warns you.
- When you compare offers, remember fees. An origination fee raises the real cost of a loan above its stated rate.
What this calculator does not include
- Fees, insurance, taxes and penalties.
- Loans with a variable rate, interest-only periods or balloon payments.
- Small rounding differences. Lenders round each payment to the cent, so the last payment can differ slightly.
This tool gives an estimate for general information only. It is not financial advice. Your lender's loan agreement has the exact figures.