Mortgage / Loan Calculator

Equal installment vs equal principal: how much extra interest you really pay

How the two repayment methods differ in math

Equal installment (often called the annuity method) has a fixed monthly payment, but its internal composition shifts: early on interest is a large share and principal a small share, and the principal share grows with every payment.

The monthly payment formula, with P the principal, i the monthly rate and n the number of periods:

Monthly = P × i × (1+i)n / ((1+i)n − 1)

Equal principal repays a fixed chunk of principal each month, equal to P / n; interest is charged on the remaining balance, so the payment falls every month:

First month = P / n + P × i, then it drops by (P / n) × i each month

In total, equal principal has a tidy closed form for its interest: Total interest = P × i × (n+1) / 2. The reason is that the balance being charged interest is an arithmetic sequence — you can also read it as "the principal declines linearly month by month".

A concrete example

Take a loan of $1,000,000 at an annual rate of 4.9% over 30 years (360 periods):

A few direct conclusions fall out of these numbers:

• The total interest is a large multiple of the principal, not loose change. On a 30-year loan at 4.9%, equal installment costs about 91% of the principal in interest. When $5,307 a month feels affordable, add the $911,000 of interest to the picture before judging.
• Equal principal saves about $174,000 in interest, at the cost of a first-month payment about 29% higher ($6,861 against $5,307). Whether you can carry that early cash pressure is the real decision, not the interest comparison alone.
• The interest gap scales with the term. A shorter term or a higher rate changes the absolute gap, but the relative pattern holds; stretch the term and the gap widens.

Which one to choose

The third row is the true decision point: money used to prepay the loan earns a "return" equal to the loan rate, risk-free. If your cash has a steadier home that beats the loan rate after tax, not prepaying is mathematically better. That comparison must use an after-tax, risk-free return as the reference — you cannot pit it against an expected stock return.

Prepayment — timing determines the saving

Equal installment front-loads interest: early payments are mostly interest, later ones mostly principal. So the benefit of prepayment decays fast with timing:

Equal principal already overpays principal every month, so its balance falls faster and the absolute interest a prepay can save is smaller — but the saving as a share still depends on timing. A second practical choice: after a prepay, do you shorten the term or reduce the monthly payment? Shortening the term saves more interest (less time the money is outstanding); reducing the payment eases cash flow. "Shorten the term to save more" usually holds, but if you are only briefly short on cash, reducing the payment is the more useful move.

Common input mistakes

• Put the monthly rate into the annual field. The tool takes an annual rate and divides by 12 internally. Typing 0.4083 (the monthly rate) makes the result about 12 times too small, producing a "almost no interest" fantasy.
• Put the term in months. 30 years means 30; typing 360 computes 360 years.
• Treat the rate as the only cost. Real loans also carry appraisal, insurance, guarantee and prepayment-penalty fees, plus rate moves from a floating rate (such as EURIBOR, SOFR or a central-bank benchmark plus a spread). The tool models pure interest, not total cost.
• Ignore what the loan amount means. Enter the loan amount (price minus down payment), not the property price. The down-payment ratio drives this number directly.
• Compare fixed and floating rates directly. A fixed rate and a floating benchmark-plus-spread rate have different future cash flows; a single-number comparison is only a snapshot of today.

How the tool works

Enter the loan principal, the annual rate (as a percent, e.g. 4.9) and the term in years; the tool shows both plans' monthly payment, total interest and total repaid, updating live. It is a general pure-interest model with no fees and no forecast of future rate moves — reliable for comparing plans and seeing the order of magnitude of interest; for signing a contract, add the actual fee clauses before you decide. All calculation runs locally; the loan amount is not uploaded.