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MasterMath

Loan Calculator

Borrow 15,000 at 8% over 5 years and you pay 304.15 a month, of which 100 is interest in the very first payment and barely 2 in the last. Work out the payment, the total cost and how it splits.

Currency and number format for

Monthly payment

—

Monthly payment—
Number of payments—
Interest paid—
Total you will repay—
The interest is—
Split of the first payment—

How this was worked out

    The formula

    payment = principal × i ÷ (1 − (1 + i)^−n)

    Where it comes from

    An amortising loan keeps the payment constant but changes what it is made of. Early on almost all of it is interest, because interest is charged on a balance that is still nearly untouched. As the balance falls, the interest share falls with it and more of each payment goes to the principal.

    How to work it out by hand

    1. Divide the annual rate by 12 to get the monthly rate
    2. Multiply the years by 12 to get the number of payments
    3. Apply the amortisation formula to get the fixed payment
    4. Multiply the payment by the number of payments to see the total cost

    What is worth knowing

    The figure worth looking at is not the monthly payment but the total interest: it is what the loan actually costs you. Two loans with almost the same payment can differ by thousands once you stretch the term, because a longer term lowers the payment and raises the cost at the same time. That is also why paying extra early is so much more effective than paying extra late: at the start you are attacking a balance that is still generating almost all the interest.

    Frequently asked questions

    Why is the first payment almost all interest?

    Because interest is charged on the outstanding balance, and at the start that balance is the whole loan. As it shrinks, so does the interest portion of each payment.

    Does a longer term make the loan cheaper?

    It makes the monthly payment smaller and the loan more expensive. You pay interest for longer, on a balance that falls more slowly.

    Is it worth overpaying?

    Almost always, and the earlier the better. An extra payment in year one removes interest that would have accrued for the whole remaining term.

    Does this include fees and insurance?

    No. It calculates the interest on the amount borrowed. Arrangement fees and required insurance raise the real cost, and the APR is the figure that includes them.