Amortization Calculator: First Payment Split and Balance
Enter the loan amount, the yearly interest rate and the number of monthly payments to see how the first payment is split between interest and principal, plus the balance left after the payments you choose.
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Formula
For a fixed-rate loan with monthly rate r = yearly rate ÷ 12 ÷ 100, n payments and loan amount P:
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
For any month: interest = balance × r, principal = M − interest, and new balance = balance − principal. At 0% interest the payment is P ÷ n. Total paid is M × n (M rounded to cents) and total interest is total paid minus P.
The balance after k payments is read from the schedule: B = P × (1 + r)^k − M × ((1 + r)^k − 1) ÷ r. It is the full loan amount at k = 0 and 0 after the last payment. At 0% interest total paid equals P exactly and total interest is 0.
Worked example
A loan of 10,000 at 12% a year, repaid over 12 months:
r = 0.01,(1.01)^12 = 1.126825M = 10,000 × 0.01 × 1.126825 ÷ 0.126825 =888.49- First month interest: 10,000 × 0.01 = 100.00, so principal is 888.49 − 100 = 788.49
- Total paid: 888.49 × 12 = 10,661.88, so interest is 661.88
- Balance after 6 payments: 10,000 × 1.01^6 − 888.49 × (1.01^6 − 1) ÷ 0.01 = 5,149.20
Frequently asked questions
What is amortization?
Amortization means repaying a loan in equal regular payments. Each payment covers the interest for the month and the rest reduces the balance, so the loan reaches zero on the last payment.
How do I split a payment into interest and principal?
Interest is the balance times the monthly rate (yearly rate ÷ 12). Principal is the payment minus that interest. For 10,000 at 12% the first interest is 10,000 × 0.01 = 100 and the principal is 888.49 − 100 = 788.49.
Why does the interest part shrink over time?
Interest is charged on what you still owe. Each payment lowers the balance, so the next month's interest is smaller and more of the same payment goes to principal.
How is the total interest worked out?
It is the monthly payment times the number of payments, minus the loan amount. A 10,000 loan at 12% over 12 months costs 888.49 × 12 − 10,000 = 661.88 in interest.