How to calculate loan payments and total interest

A loan payment does two jobs: it pays interest, and it reduces the amount you owe. With a fixed-rate amortizing loan, the payment stays level, but those two parts change. Let us calculate a twenty-thousand-dollar loan at six percent annual interest, repaid monthly over five years.

Start with the principal, meaning the amount actually borrowed. Convert six percent to zero point zero six, then divide by twelve. The monthly rate is zero point zero zero five, or half a percent. Five years times twelve gives sixty payments. The rate and the number of payments must use the same period.

The monthly payment equals principal times the monthly rate, divided by one minus, one plus the monthly rate, raised to the negative number of payments. This formula chooses a level payment that brings the balance to zero. Substitute twenty thousand, zero point zero zero five, and sixty. The estimated payment is three hundred eighty-six dollars and sixty-six cents.

For month one, interest is the starting balance times the monthly rate. Twenty thousand times zero point zero zero five is one hundred dollars. Subtract that from the payment. About two hundred eighty-six dollars and sixty-six cents repays principal. The remaining balance is about nineteen thousand seven hundred thirteen dollars and thirty-four cents.

In month two, interest is calculated on that smaller balance: about ninety-eight dollars and fifty-seven cents. More of the same payment now reduces principal. Repeat: calculate interest, subtract it from the payment, and reduce the balance. Across the schedule, the interest portion shrinks and the principal portion grows. That changing split is amortization.

To estimate total payments, multiply the unrounded monthly payment by sixty. That is about twenty-three thousand one hundred ninety-nine dollars. Subtract the twenty-thousand-dollar principal. Total interest is about three thousand one hundred ninety-nine dollars. Keep full precision until the final answer; rounding every payment to cents can slightly change the last payment.

What if the same loan lasts six years? Keep the amount and rate unchanged, but use seventy-two payments. The payment falls to about three hundred thirty-one dollars and forty-six cents. Total interest rises to about three thousand eight hundred sixty-five dollars. A longer term lowers the monthly burden while keeping a balance outstanding longer.

This example assumes a constant interest rate, monthly payments at the end of each period, and no fees or extra payments. Use the loan interest rate for this model. A disclosed A P R can include fees and may differ from that rate. Daily-interest loans can also depend on payment dates. At zero interest, simply divide principal by the number of payments.

Remember three inputs: the amount borrowed, the rate per payment period, and the number of payments. Calculate the level payment, then split each payment into interest and principal. Finally, compare both the monthly payment and total interest. In our five-year example, the payment is about three hundred eighty-six dollars and sixty-six cents, with about three thousand one hundred ninety-nine dollars in total interest.