Every loan payment you make is calculated using a formula that your lender knows, understands, and uses to structure your payment schedule. You can learn it too.
The formula is not complicated. Once you know it, you will never be surprised by a payment amount again.
The Formula
M = P × [r(1+r)^n] / [(1+r)^n − 1]
Where:
- M = your monthly payment
- P = the principal (amount you borrow)
- r = your monthly interest rate (annual rate ÷ 12)
- n = total number of payments (loan term in years × 12)
Working Through It
You borrow $200,000 at 6% annual interest on a 30-year mortgage.
r = 0.06 ÷ 12 = 0.005
n = 30 × 12 = 360
M = 200,000 × [0.005(1.005)^360] / [(1.005)^360 − 1]
M = 200,000 × [0.005 × 6.0226] / [6.0226 − 1]
M = 200,000 × 0.03011 / 5.0226
M = $1,199.10 per month
That number covers both principal and interest. In the early months, most of each payment goes to interest. Over time, that flips — but the total monthly amount stays fixed.
Why Banks Do Not Want You to Know This
Banks provide your payment amount. They rarely show you the amortization breakdown: how much of each payment is principal versus interest, and how the split changes over time.
With that breakdown, you can answer questions like:
- How much do I save by making one extra payment per year?
- How much faster do I pay off the loan if I round up my payment?
- What does the bank make in total interest over 30 years?
That last number is the one worth knowing. On a $200,000 mortgage at 6% over 30 years, you pay $231,676 in interest — more than the original loan amount.
The Extra Payment Effect
Adding $100 to each monthly payment on that same mortgage:
- Total interest saved: $28,239
- Loan term shortened by: 4 years, 2 months
Even $50/month makes a real difference over 30 years.
Where the Formula Breaks Down in Practice
The formula assumes a fixed rate. For adjustable-rate mortgages (ARMs), the rate changes at set intervals and the formula needs to be recalculated each time.
It also assumes you pay on schedule. Late payments, deferment, or forbearance all add interest that the basic formula does not account for.
Calculate It Automatically
The Loan Calculator applies this formula instantly and shows your full amortization schedule. No signup, no math required.
Related tools:
- Loan Calculator — monthly payment, amortization, extra payment scenarios
- Mortgage Calculator — for home purchase planning
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