MISSION · Number sense
Loans, Credit and the Cost of Borrowing
Where a monthly payment goes, and why it is mostly interest at first
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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The idea in one sentence
A loan payment is split in two — interest on what you still owe, then whatever is left over knocks down the balance — and early on, almost all of it is the first part.
The monthly rate
Interest is quoted annually as an APR, but charged monthly. Divide:
\[\text{monthly rate} = \frac{\text{APR}}{12}\]12% APR is 1% a month. Borrow $1000 and the first month’s interest is $10.
Strictly, twelve months of 1% compounds to \(1.01^{12} - 1 = 12.68\%\), not 12%. That figure is the APY or effective rate, and it is the one that tells you what you will really pay. Lenders advertise the smaller number, savings accounts advertise the larger one, and both are describing the same arithmetic.
Where a payment goes
Each month, in this order:
- Interest is charged on the current balance.
- Your payment covers that interest first.
- Whatever remains reduces the principal.
$1000 at 1% a month, paying $100:
| Month | Balance | Interest | To principal | New balance |
|---|---|---|---|---|
| 1 | 1000.00 | 10.00 | 90.00 | 910.00 |
| 2 | 910.00 | 9.10 | 90.90 | 819.10 |
| 3 | 819.10 | 8.19 | 91.81 | 727.29 |
The payment never changes, but its split shifts steadily. This is amortisation, and the shift is slow at the start and fast at the end — which is why three years into a long mortgage the balance has barely moved, and why that feels unfair without being a trick.
The minimum payment trap
Credit cards set a minimum near 2% of the balance, and at 18% APR — 1.5% a month — the interest alone eats most of it.
On a $1000 balance: the minimum is $20, the interest is $15, and $5 comes off the principal. At that rate the debt takes 94 months — nearly eight years — to clear, and the $862 of interest is almost as much again as the thing you bought.
The lesson is not about willpower. It is that anything above the minimum goes entirely to principal, so it is worth far more than its size suggests. Paying $40 instead of $20 does not halve the time — it cuts it by much more, because the extra $20 is pure principal while the first $20 was mostly interest.
Comparing offers honestly
Term length. A longer term means a smaller monthly payment and more total interest. The two move in opposite directions, and the monthly figure is the one advertised.
Total cost. Multiply the payment by the number of payments. A $1000 loan repaid at $100 for 11 months costs $1100; the same loan at $50 for 24 costs $1200.
Fees and APR. A stated APR should include compulsory fees, which is what makes it comparable between lenders in a way that a headline rate is not.
0% offers. Usually real, usually time-limited, and usually followed by a high rate applied to whatever is left — sometimes backdated to the start.
Common mix-ups
- Using the APR as the monthly rate. Divide by 12 first.
- Charging interest on the original amount rather than the current balance. That is simple interest, and loans are not simple interest.
- Reading a small monthly payment as a cheap loan. It usually means a longer term and more interest.
- Thinking the minimum payment is the recommended payment. It is the smallest the lender will accept, chosen to maximise what they earn.
- Comparing a monthly rate to an APR from another offer. Put both on the same footing first.
Check yourself
What is the monthly rate on 12% APR, what does the remainder of a payment reduce after interest is taken, and what does paying only the minimum do to total interest?
\(\frac{12\%}{12} = 1\%\) a month. Interest comes off first and the rest reduces the principal. And minimum payments stretch the loan out, so the total interest paid is larger.
LEVEL 3 · REFLECT
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