“You’re approved — but what will the monthly payment actually be?” “How much of what I repay is interest?” A loan’s numbers can feel like they belong to the lender alone. In fact, the most common repayment style follows one formula you can learn in a few minutes.
This guide walks through the annuity (equal-payment) formula that sits behind most car and home loans, works through a full example on a 1,000,000 yen loan, and shows how interest rates and terms move both the monthly payment and the total cost. A free browser calculator does the arithmetic for you at the end.
What Annuity Repayment Is — and the Formula
First, the vocabulary:
- Principal: the amount borrowed
- Interest: the cost of borrowing, charged on the remaining balance
- Monthly rate: the annual rate divided by 12
Under annuity repayment, every payment is the same size. Each month, the payment first covers the interest accrued on the outstanding balance, and whatever remains reduces the principal. Early payments are therefore interest-heavy; as the balance shrinks, more of each payment goes to the principal. This is the standard structure for home and car loans.
The monthly payment comes from this formula:
monthly payment = amount × monthly rate × (1 + monthly rate)^n ÷ ((1 + monthly rate)^n − 1)
where n is the number of payments. It is the same arithmetic used for annuities: the fixed payment that pays back an amount plus interest evenly across n installments.
| Style | Monthly payment | Character | Where you’ll see it |
|---|---|---|---|
| Annuity (equal payment) | Constant | Interest-heavy early on; easy to plan around | Standard for home and car loans |
| Equal principal | Decreases | Heavier at first, but less total interest | Some home and business loans |
Worked Example: 1,000,000 Yen at 5% for 5 Years
Following the formula step by step for a 1,000,000 yen loan at 5% annually over 60 months:
- Monthly rate: 5% ÷ 12 = 0.4167% (0.004167)
- (1 + monthly rate) to the 60th: 1.004167^60 ≈ 1.2834
- Numerator: 1,000,000 × 0.004167 × 1.2834 ≈ 5,347
- Denominator: 1.2834 − 1 = 0.2834
- Divide: 5,347 ÷ 0.2834 ≈ 18,871
The monthly payment is about 18,871 yen. Sixty of those payments total roughly 1,132,274 yen, which makes the total interest about 132,274 yen — roughly 13% of the amount borrowed added on top.
The totals follow two simple steps:
- Total repayment = monthly payment × number of payments
- Total interest = total repayment − principal
Shorten the same loan to 3 years and the payment rises to about 29,971 yen (total 1,078,952 yen, interest 78,952 yen). The monthly burden grows by roughly 60%, while total interest drops by about 53,000 yen. That trade-off between monthly burden and total interest is the axis on which every term decision turns.
Reading the numbers: Longer terms lower the monthly payment but increase total interest, because you're renting the money for more months. Halving the term roughly halves the payment — but it cuts total interest by more than half. Always read the two figures together.
For scale, a 30,000,000 yen home loan at 3% over 35 years (420 payments) under annuity repayment runs about 115,455 yen per month, totalling roughly 48,491,124 yen — with about 18,491,124 yen of interest. Interest exceeding the original loan is exactly why rate and term negotiation, and early repayments, matter so much on big loans.
These are estimates: Lenders round differently, accrue interest daily, add fees, and may structure bonus payments — so real quotes can differ from these figures by a small amount. Confirm exact numbers with your lender's own simulation before signing. Nothing in this article is a recommendation of a specific financial product.
Calculate a Loan in Your Browser
In practice, you’ll want the arithmetic done for you. The Tools Hub loan repayment calculator takes the amount, rate and term, and instantly shows the monthly payment, total repayment, total interest — plus a year-by-year schedule of payments, interest and remaining balance. Everything runs in your browser; nothing you enter is transmitted.
The schedule table makes the shift from interest-heavy to principal-heavy payments visible, which is also why early extra repayments are so effective: they attack the balance while it’s still large.
How to use it (3 steps)
Enter amount and rate
Open the loan calculator and fill in the loan amount and annual interest rate. 0% loans are supported.
Set the term
Specify the term in years plus any extra months — 5 years is years 5, months 0; 1 year 3 months is years 1, months 3.
Review the schedule
Check the monthly payment alongside the yearly table of payments, interest and balance to see how the payoff actually progresses.
Tool mentioned in this article
Loan Repayment Calculator
Monthly payment, total interest and a yearly schedule — instant, in your browser, free.
Once you have a payment figure in mind, the discount calculator and tax calculator help you work backwards from sticker prices to what you’d actually finance.
Summary
- Annuity repayment keeps the monthly payment constant — the standard for home and car loans
- monthly payment = amount × monthly rate × (1 + rate)^n ÷ ((1 + rate)^n − 1)
- 1,000,000 yen at 5% for 5 years ≈ 18,871 yen/month, with about 132,274 yen total interest
- Longer terms lighten the month but grow the interest — read both figures together
- A yearly balance schedule shows when extra repayments bite hardest
- Tools Hub’s loan calculator does all of it free, in the browser
Enter your real amount and rate, then compare a few terms — the repayment picture gets concrete fast.
FAQ
Which is better: annuity or equal-principal repayment?
At the same rate and term, equal-principal repayment accrues less total interest because it reduces the balance faster early on. The trade-off is a heavier starting payment. Neither style is objectively better — it depends on income stability and how front-loaded a payment you can sustain.
Can I calculate the effect of an early repayment?
Yes. Interest accrues on the remaining balance, so after a lump-sum payment, recalculate from the new (smaller) balance and the savings fall out of the math. The yearly balance column in the calculator’s schedule shows why early repayments — while the balance is still large — save the most interest.
What about a 0% interest loan?
With no interest, the monthly payment is simply the amount divided by the number of payments. A 120,000 yen loan over 12 months costs 10,000 yen per month, and total interest is zero. The calculator handles 0% as well.
Does this work for variable-rate loans?
Variable rates mean the payment gets recalculated when the rate changes, so a calculation at today’s rate is a “if rates stay here” baseline. It’s good practice to also run the numbers at a rate one or two steps higher to see how the payment would move.
