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Interest and overpay: why the same rate is not the same cost of a loan
You took a loan, you pay every month on time, and the debt shrinks much slower than you expected. Where does the money go?
The payment has two parts. One returns the money you borrowed. The other pays for using it — that is interest.
How those parts split depends on the repayment schedule. We will look at two common schemes: annuity and reducing (differentiated). The names are heavy; the idea is plain.
Principal and interest: what you are paying
Principal, or the body of the loan, is the money you borrowed and have not yet returned.
If the bank gave you $280,000, the starting principal is $280,000. When part of a payment goes to that, the remaining debt falls.
Interest is the fee for using the bank’s remaining money. Paying it does not by itself reduce the principal.
Say you paid about $2,702. About $2,333 of that went to interest, and $369 to principal. Together that is one payment, but the debt fell only by $369.
So “I sent the bank a million” and “I repaid a million of principal” are different things.
What sets the interest amount
With ordinary repayment, interest is charged on the remaining principal. The larger that remainder, the higher the fee for using the money at the same rate.
A simple monthly picture looks like this:
Interest for the month = remaining principal × annual rate ÷ 12.
For example, with $280,000 of debt and a 10% annual rate:
$280,000 × 10% ÷ 12 ≈ $2,333.
If the remaining debt falls to $140,000, the same calculation gives about $1,167 a month.
A real bank schedule may depend on the days between payments and the contract rules. The principle stays: a smaller remainder means less interest charged, other things equal.
That is why the speed of returning principal so strongly changes the overpay.
Annuity payment: the same amount every month
An annuity schedule means that, if the terms stay the same, you pay roughly the same amount every month.
That is handy for a budget. You know how much to set aside for the loan and can plan the rest of the money in advance.
A constant payment amount does not mean a constant mix.
At the start the debt is large, so a lot of interest is charged on it. A smaller share of the payment is left to return the principal itself.
The debt then shrinks. Interest becomes smaller, and more of the payment goes to principal. The total payment stays the same.
Early on, most of the payment can go to interest; near the end, most goes back to principal.
That does not mean the bank first takes all interest for future years. Each period you pay the interest charged on the remaining debt. At the start that debt is simply especially large.
Reducing payment: the amount falls over time
On a reducing schedule the principal is split into equal parts by the number of months. Each month you return one such part and also pay interest on the remainder.
Say you borrowed $280,000 for 20 years. That is 240 months.
The monthly return of principal will be:
$280,000 ÷ 240 ≈ $1,167.
That part stays the same. Interest falls over time because the debt is smaller every month.
So the first payments are the largest, and the last are the smallest.
For a budget, the start of such a loan is heavier. But principal shrinks faster from the first months than on an annuity schedule with the same amount, rate and term.
One loan — two different schedules
Take the same terms:
- Loan amount — $280,000.
- Rate — 10% a year.
- Term — 20 years, or 240 months.
- Monthly payments, no early repayment.
For the comparison we use a monthly rate of 10% ÷ 12. Insurance, fees and other costs are left out: here we compare only repayment of principal and the charging of interest.
| Figure | Annuity schedule | Reducing schedule |
|---|---|---|
| First payment | ≈ $2,702 | $3,500 |
| Interest in the first payment | ≈ $2,333 | ≈ $2,333 |
| Principal in the first payment | ≈ $369 | ≈ $1,167 |
| Payment in month 120 | ≈ $2,702 | ≈ $2,343 |
| Last payment | ≈ $2,702 | ≈ $1,176 |
| All payments over 20 years | ≈ $648,400 | ≈ $561,200 |
| Interest overpay | ≈ $368,400 | ≈ $281,200 |
The figures are rounded. A bank’s own schedule may differ a little because of accrual dates and rounding.
At the same rate the gap in interest is about $87,200.
The reason is the speed of returning the money. On a reducing schedule the borrower returns a larger share of the debt earlier. So in later months interest is charged on a smaller amount.
Why interest is the same in the first month
In both schemes the starting debt is the same — $280,000. The rate and the calculation period are the same too. So interest for the first month matches.
What differs is the amount you send back toward the principal itself.
On the annuity schedule that is about $369. On the reducing schedule — about $1,167.
After the first payment the remainders already differ. From the next month the interest charged differs too. Then the gap accumulates.
The smaller overpay comes because at the start you give the bank more money and shrink the debt faster.
Halfway through the term is not always half the debt repaid
A 20-year loan has run for 10 years. It seems logical that half the principal is already back.
On a reducing schedule that is true: you return the same slice of principal every month. After 120 of 240 payments, $140,000 is repaid and $140,000 remains.
On the annuity schedule in our example, the first 10 years repay about $75,600 of principal. The remainder is about $204,400.
Payments were regular, yet a large share of the money went to interest. Principal repayment speeds up later, when charged interest takes a smaller share of the fixed payment.
So if you want to know how much you still owe, look at the remaining principal, not only at how many years have passed.
How to read the overpay
Interest overpay is the sum of interest over the whole term of the loan.
If you borrowed $280,000 and paid the bank about $648,400, of that:
- $280,000 — repayment of the money borrowed;
- about $368,400 — interest.
Total payments and overpay are different figures. They are easy to mix up, especially when both are large.
And to judge all costs of the loan you still need to count extra payments if the contract has them. In our example there are none.
One more: a 10% annual rate does not mean that over 20 years you simply pay 200% of the starting amount. The remaining debt changes after every payment. For an exact figure you need the repayment schedule.
Which scheme fits you
With the same amount, rate and term, and with no early payments, a reducing schedule gives a smaller interest overpay. But you have to stand higher payments at the start.
In our example the first payment is $3,500 instead of about $2,702. The gap is almost $800 a month — a real load for a household.
An annuity schedule is easier when you need a predictable monthly amount. It helps plan the budget and asks for a smaller first payment.
So it helps to compare both sides of the choice: how much you will pay over the whole term, and how much you can give now. Saving on interest will not help if the first payments are too heavy.
You also need to check whether the bank offers both options. Not every loan product lets you choose the schedule.
When you compare offers, look at the amount, the rate, the term, extra costs and the order of payments together. Otherwise you can take a difference in terms for an advantage of one scheme.
What to check in your own schedule
Open the repayment schedule and find three figures: how much goes to interest, how much to principal, and what remainder is left after the payment.
Then look at the first month, the middle of the term and the last month. That shows how your loan changes.
The same monthly payment does not mean the debt falls by the same amount every month. And the same rate does not mean the same overpay. What decides it is how much money you return and how long you use what is left.