How a Monthly Loan Payment Is Calculated (With Example)
The amortisation formula behind every fixed-rate loan, with a worked NT$1,000,000 five-year example and how rate changes affect the payment.
The formula
For a fixed-rate loan with equal monthly payments: payment = P × r ÷ (1 − (1 + r)^−n), where P is the amount borrowed, r is the monthly rate (annual rate ÷ 12) and n is the number of months.
Worked example
Borrow NT$1,000,000 at 2.5% a year for 60 months. r = 0.025 ÷ 12 = 0.002083. The payment is about NT$17,747 a month, so total repayment is about NT$1,064,842 and total interest about NT$64,842.
What changes the payment
At 3.5% the same loan costs about NT$18,192 a month. A longer term lowers the payment but increases total interest, because interest is charged on the balance for more months.
Before you sign
Lenders may add fees, insurance or a different compounding rule, so ask for the annual percentage rate and the full repayment schedule.
Try it
The loan payment calculator shows the monthly payment, total repayment and total interest for any amount, rate and term.