How to Calculate a Loan Payment: Formula and Worked Examples
Every loan payment — mortgage, car, personal, student — comes from one formula, and understanding it explains why early payments are mostly interest, why a longer term costs so much more, and why extra payments are so powerful. This guide derives the formula, works it on real loans, and shows the amortisation pattern it produces.
Key takeaways
- Monthly payment = P × (i(1+i)ⁿ) / ((1+i)ⁿ − 1), where P is principal, i is the monthly rate, and n is the number of payments.
- Early payments are mostly interest because interest is charged on the full balance; as the balance falls, the principal slice grows and the interest slice shrinks.
- Extra payments attack principal directly and shorten the loan disproportionately: $100 extra a month on a 30-year mortgage can cut years off the term and tens of thousands off total interest.
The formula, derived in one paragraph
A loan is an exchange: the lender gives P today, and you repay it as n equal monthly payments M. Each payment must cover that month’s interest plus a slice of principal, and the present value of all payments (discounted at the monthly rate i) must equal P. Summing the geometric series of discounted payments and solving for M gives the standard formula:
M = P × (i × (1 + i)ⁿ) / ((1 + i)ⁿ − 1)
Here i is the monthly rate — the annual rate divided by 12 — and n is the total number of monthly payments (years × 12). The formula assumes a fixed rate, level payments, and no fees or extra charges; adjustable rates, balloon payments, and fees all sit outside it. The loan payment calculator on this page evaluates it for any principal, rate, and term, with a full amortisation schedule.
Worked examples
Mortgage: $300,000 at 6% for 30 years (360 payments). Monthly rate i = 0.005. (1.005)³⁶⁰ ≈ 6.0226. M = 300,000 × (0.005 × 6.0226)/(6.0226 − 1) = 300,000 × 0.030113/5.0226 ≈ $1,798.65. Total paid: $647,514; total interest: $347,514 — more than the principal itself.
Car loan: $25,000 at 7% for 60 months. i = 0.07/12 ≈ 0.005833. (1.005833)⁶⁰ ≈ 1.4176. M = 25,000 × (0.005833 × 1.4176)/(0.4176) ≈ $495.03. Total paid ≈ $29,702; interest ≈ $4,702.
Personal loan: $15,000 at 11% for 36 months. i ≈ 0.009167. (1.009167)³⁶ ≈ 1.3881. M = 15,000 × (0.009167 × 1.3881)/(0.3881) ≈ $491.10. Total paid ≈ $17,680; interest ≈ $2,680.
Short vs long, same mortgage: $300,000 at 6% for 15 years (180 payments): M ≈ $2,531.57, total interest ≈ $155,683. The 15-year payment is 41% higher monthly but total interest is less than half the 30-year figure — the term effect, quantified.
Why early payments are mostly interest
Each month’s interest is the current balance × monthly rate. On the $300,000, 6% mortgage, month 1 interest is $300,000 × 0.005 = $1,500, leaving only $298.65 of the $1,798.65 payment for principal. Month 2 interest is $299,701.35 × 0.005 ≈ $1,498.51, leaving $300.14 for principal. The principal slice grows by roughly the monthly rate each month (it compounds: each month’s principal slice is the previous month’s times (1 + i)), while the interest slice shrinks correspondingly. Halfway through a 30-year loan, the payment is still mostly interest; the crossover — where principal exceeds interest — arrives around year 19 for a 6% 30-year loan. This pattern is not a lender trick; it is arithmetic, and it is why “I’ve paid for years but barely dented the balance” is a normal experience, not a scam.
What a longer term really costs
| Term ($300,000 at 6%) | Monthly payment | Total interest |
|---|---|---|
| 15 years | $2,531.57 | $155,683 |
| 20 years | $2,148.46 | $215,630 |
| 30 years | $1,798.65 | $347,514 |
Extending from 15 to 30 years cuts the payment by 29% but more than doubles total interest. The trade is real: a lower payment buys monthly breathing room at a large total price. Choose the shortest term whose payment fits comfortably — “comfortably” meaning with a margin for rate rises (on adjustable loans), income shocks, and the other costs of the purchase — not the longest term whose payment merely fits.
Extra payments: the disproportionate payoff
Extra payments go entirely to principal (confirm your lender applies them that way — some apply extra amounts to future payments instead, which does not shorten the loan). Because principal slices compound, an extra payment early is worth more than the same amount later: it removes not just itself from the balance but all the interest that balance would have accrued.
On the $300,000, 6%, 30-year mortgage ($1,798.65 a month), adding $100 a month to principal pays the loan off about 5 years early and saves roughly $75,000 of interest. Adding $200 a month pays it off about 8–9 years early and saves roughly $115,000. A single $5,000 lump sum in year 1 saves about $15,000 of interest over the loan’s life and shortens it by roughly a year. These are approximations — exact figures depend on timing and lender application — but the direction and scale are robust: small, early, consistent extra principal is the highest-return use of spare cash most borrowers have, beating savings-account returns by the mortgage rate, risk-free and tax-aware (mortgage interest deductibility, where applicable, slightly reduces the effective return, but rarely below the value of the saving).
Frequently asked questions
What is the loan payment formula?
M = P × (i(1+i)ⁿ) / ((1+i)ⁿ − 1), where P is the principal, i is the monthly interest rate (annual rate ÷ 12), and n is the number of monthly payments. For $300,000 at 6% over 30 years, M ≈ $1,798.65.
Why is my early payment mostly interest?
Because monthly interest is charged on the current balance, which is largest at the start. On a $300,000, 6% mortgage, month 1 interest is $1,500 of the $1,798.65 payment; the principal slice grows each month as the balance falls.
How much does a longer term cost?
On $300,000 at 6%, a 30-year term costs $347,514 of interest versus $155,683 for 15 years — more than double — while cutting the monthly payment by only 29%.
Do extra payments really help that much?
Yes, disproportionately: $100 extra a month on a $300,000, 6%, 30-year mortgage pays it off about 5 years early and saves roughly $75,000 of interest, because extra principal removes all its future interest too. Confirm your lender applies extra amounts to principal.
What is amortisation?
The schedule by which a loan is paid off through regular payments, each split between interest (on the current balance) and principal. Early payments are interest-heavy; late payments are principal-heavy.
Does the formula work for car and personal loans?
Yes — the same formula governs any fixed-rate, level-payment loan. Only the principal, rate, and term change. Adjustable rates, fees, and balloon payments sit outside it.
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