Loan Calculator

The formula, applied to the starting example

The payment comes from the standard amortising formula M = P × r ÷ (1 − (1 + r)^−n), where P is the amount, r is the monthly rate (annual rate ÷ 12 ÷ 100) and n is the number of monthly payments (years × 12).

With the values the calculator opens with, 20,000 at 6.5% over 5 years: r = 0.065 ÷ 12 = 0.0054167 and n = 60. (1 + r)^−60 = 0.72316, so the denominator is 1 − 0.72316 = 0.27684. The numerator is 20,000 × 0.0054167 = 108.33, and 108.33 ÷ 0.27684 = 391.32 per month. Sixty payments total 23,479.38, of which 3,479.38 is interest.

When the rate is 0 the formula would divide by zero, so the tool switches to a straight split: 12,000 over 3 years is 12,000 ÷ 36 = 333.33 a month with no interest at all.

How the term changes what you pay

Stretching the same loan from 3 to 7 years roughly halves the monthly payment but more than doubles the interest, from about 2,067 to about 4,947. The calculator is quickest way to see that trade-off: change only the term and watch the Total interest box.

How the rate changes what you pay

Each extra percentage point on a five-year 20,000 loan adds roughly 9 to 10 to the monthly payment and 550 to 600 to the interest bill, which is why a slightly better rate from a second lender is worth the paperwork.

How each payment splits between interest and principal

The payment never changes, but its make-up does. Interest for any month is the remaining balance times the monthly rate, so it starts at 108.33 and shrinks as the balance falls, while the principal share grows from 282.99 to 389.21. The page shows only the three summary boxes, not this month-by-month schedule, but you can reproduce any line from the balance and the rate.

What the estimate leaves out

• Origination or arrangement fees, insurance and late charges. If a fee is rolled into the loan, add it to the amount you enter.
• Variable rates. The rate you type is assumed to hold for the whole term.
• Overpayments and early settlement, which reduce the interest below the figure shown.
• Lenders' exact day-count and rounding conventions, which can move a payment by a few cents.
• The boxes are formatted as US dollars whatever you actually borrow in. The arithmetic is unit-free, so read the symbol as your own currency.
• Leaving the amount or the term empty, or setting either to 0, hides the result boxes until you fill them in.

Checking a quote against this calculator

Enter the headline figures from the offer. If the lender's monthly payment is higher than the one shown here, the difference usually comes from fees being financed, a rate quoted monthly rather than annually, or payment protection insurance bundled into the instalment. Ask for the APR, which includes most compulsory fees, and try it here as the rate to see how close the two numbers get.