Loan Calculator

Loan calculator at a glance#

What is the monthly payment on a $31,000 loan over 5 years?#

At an example rate of 8%, a $31,000 loan over 5 years costs $628.57 a month, with $6,714.09 in total interest. Enter your own amount, rate and term in the calculator above to get the payment, the total interest and a full amortization schedule. This gives an estimate, not financial advice.

What is the monthly payment on a $27,000 loan for 5 years?#

At an example rate of 8%, a $27,000 loan over 5 years costs $547.46 a month, with $5,847.76 in total interest and $32,847.76 paid in all. The rate you're offered changes it: at 6% the payment is $521.99, at 10% it's $573.67 and at 12% it's $600.60.

How much interest will you pay on a loan?#

The calculator shows it as Total Interest. By hand, multiply the monthly payment by the number of payments and subtract the amount borrowed: 60 × $547.46 is $32,847.60, so about $5,848 of it is interest. The calculator's $5,847.76 uses the unrounded payment, which is why the cents differ slightly.

How a loan payment is split#

The calculator treats a loan as amortized. You pay the same amount every month, and each payment first covers the interest charged on the balance that month. Whatever is left pays down the principal, the amount you still owe.

Take the example loan. In month 1 the interest is $27,000 × 0.08 ÷ 12 = $180.00. The other $367.46 of the $547.46 payment reduces the balance to $26,632.54. In month 2 the interest is charged on that smaller balance, so it drops to $177.55 and $369.91 goes to principal. By payment 30 the split is $101.91 interest and $445.55 principal, and the final payment carries only $3.63 of interest.

The Consumer Financial Protection Bureau describes the same pattern in its explanation of amortization: early payments go mostly to interest, and the balance falls slowly at first and faster near the end of the term.

The loan payment formula, step by step#

The monthly payment comes from one formula, the same one used in the loans chapter of OpenStax Contemporary Mathematics:

M = P × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1)

Here's the $27,000 example at 8% for 5 years worked through:

1. Monthly rate: r = 0.08 ÷ 12 = 0.0066667
2. Number of payments: n = 5 × 12 = 60
3. Growth factor: (1 + r)⁶⁰ = 1.48985
4. Top of the fraction: 0.0066667 × 1.48985 = 0.0099323
5. Bottom of the fraction: 1.48985 − 1 = 0.48985
6. Payment: $27,000 × 0.0099323 ÷ 0.48985 = $547.46

The fraction on the right is the payment per dollar borrowed, 0.020276 here. Multiply it by any amount at the same rate and term and you get that loan's payment, so $10,000 at 8% for 5 years is $202.76 a month.

How the balance falls over the life of the loan#

Because each month's interest is charged on what you still owe, the interest part shrinks every year and the principal part grows. On the example loan you pay about $1,995 of interest in year 1 and only $276 in year 5, while the payment stays at $547.46 the whole time.

The balance follows the same curve. It's $22,425.12 after the first year, $12,104.70 after three years and zero after the 60th payment. The schedule under the results lists every payment with its beginning balance, interest, principal and ending balance, so you can see exactly where you stand at any point. The amortization calculator shows the same kind of schedule grouped by year as well as by month.

Monthly payments for common loan amounts#

The table shows the monthly payment for loan amounts from $5,000 to $50,000 over 3, 5 and 7 years. Every value uses an example rate of 8% with monthly payments and comes from the same formula as the calculator. It is not a rate quote, so enter the rate you're offered above for your real figure.

A $38,000 loan over 5 years at 8% is $770.50 a month. A $31,000 loan over the same 5 years is $628.57, and $6,500 is $131.80. If your amount sits between two rows, the payment scales in step with the amount: a loan twice as large has a payment twice as large at the same rate and term.

Rate, term and the total cost#

A longer term lowers the monthly payment and raises the total interest. On $27,000 at 8%, a 3-year term costs $846.08 a month and $3,458.95 in interest. Five years drops the payment to $547.46 but lifts interest to $5,847.76, and seven years gives $420.83 a month with $8,349.53 of interest. The payment calculator page compares how much the rate and the term each move the payment.

The rate works on both numbers at once. Each step up in the rate raises the payment and the total interest together, which is why comparing offers on the APR matters. The APR calculator adds a loan's fees to its rate to show what the money really costs.

Payment frequency and compounding options#

Under Options you can set the payment schedule anywhere from daily to yearly, including every 2 weeks and twice a month. Interest compounding has its own setting. It starts at Monthly (APR) and goes from daily to annually, plus continuously. If you pay on one schedule and interest compounds on another, the calculator first turns the annual rate into an equivalent rate per payment, then applies the formula.

Paying the example loan every 2 weeks with monthly compounding gives 130 payments of $252.22 and $5,789.00 in total interest. Keeping monthly payments but switching to daily compounding gives $547.80 a month and $5,867.80 of interest.

What this calculator leaves out#

The calculator assumes a fixed rate and equal payments from start to finish. It has no field for fees, so an origination fee or other charge isn't part of its totals. It also has no extra payment field. For loans with a down payment, trade-in and sales tax, the auto loan calculator handles those inputs, and the personal loan calculator adds a start date and shows the month of your final payment.

Sources#

• OpenStax, Contemporary Mathematics, 6.8 The Basics of Loans (loan payment formula and amortization)
• Consumer Financial Protection Bureau, What is amortization and how could it affect my auto loan?
• Consumer Financial Protection Bureau, What is the difference between a loan interest rate and the APR?

Frequently asked questions#

What is the monthly payment on a $38,000 loan for 5 years?#

At an example rate of 8%, it's $770.50 a month, with $8,230.18 in total interest. Over 7 years the payment falls to $592.28 but the interest rises to $11,751.20.

How much are the payments on a $6,500 loan?#

At an example rate of 8%, a $6,500 loan costs $203.69 a month over 3 years, $131.80 over 5 years or $101.31 over 7 years.

What is the monthly payment on a $70,000 loan?#

At an example rate of 8%, a $70,000 loan is $1,419.35 a month over 5 years, with $15,160.86 of interest. Over 7 years it's $1,091.04 a month and $21,646.94 of interest.

Why does so much of my early payment go to interest?#

Interest is charged on the balance you still owe, and the balance is largest at the start. On the example loan the first payment carries $180.00 of interest. As you pay the balance down, the interest part shrinks and more of each payment reduces the principal.

Is the interest rate the same as the APR?#

No. The APR adds the loan's fees, such as origination charges, to the interest rate, and the APR calculator works it out for you.

Does the calculator work for pounds or other currencies?#

Yes. The formula doesn't depend on the currency, so enter the amount in pounds, euros or any other currency and read the results in that currency. The calculator labels amounts with a dollar sign.

Can I see a full amortization schedule?#

Yes. Below the results, the calculator lists every payment with its beginning balance, interest, principal and ending balance, and it charts the balance, the interest paid and the principal paid over the term.