Each repayment has two jobs: A repayment usually covers interest first, then reduces the principal still owed.
| Part of repayment | Purpose |
|---|---|
| Interest part | cost of borrowing |
| Principal part | reduces the loan balance |
The loan balance falls over time: As the balance falls, the interest part usually becomes smaller.
Concept example
A monthly repayment is $400.
If $120 is interest, how much reduces the principal?
Step by step
- Principal reduction = repayment - interest.
Final answer
$280 reduces the principal.
Do not call the whole payment interest: Only part of the repayment is interest.
The rest actually pays off the loan.
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Amortization: Amortization means gradually reducing a loan through regular repayments until the balance reaches zero.
| Early in loan | Later in loan |
|---|---|
| Higher balance, so often more interest | Lower balance, so often less interest |
| Smaller share paying off principal | Larger share paying off principal |
Read the table language: IB may give repayment tables, balance schedules, or plain-language descriptions.
The structure idea is the same.
| Term | Meaning |
|---|---|
| Principal | The amount borrowed — or the amount still to be repaid |
| Interest | The cost of borrowing — charged as a percentage of the balance |
| Repayment | The regular payment made each period (e.g. monthly) |
| Amortization | The process of gradually clearing the loan through repayments |
If the repayment is $500 and the interest charge is $140, how much of the principal is reduced?
$500 − $140 = $360. That $360 goes toward reducing the loan balance.
What happens to the loan balance over time in amortization?
It gradually falls toward zero. Each repayment reduces the balance a little more.
Why does the interest portion of a repayment often shrink over time?
Because interest is charged on the remaining balance. As the balance falls, so does the interest part — meaning more of each payment goes toward the principal.
Interpretation example
Why might the same monthly repayment clear more principal later in the loan?
Step by step
- Because the outstanding balance is smaller later on.
- That usually means less interest is charged in that period.
Final answer
More of the repayment can go toward principal later in the loan.
This is a pattern question: You do not always need a full amortization table.
Sometimes IB just wants you to explain the pattern.
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LOAN REPAYMENT QUESTION: You want to buy something. You cannot afford the full price at once.
You pay part of the price now — this is the deposit. You borrow the rest from a bank.
The bank charges interest. You pay the loan back in equal monthly payments.
The exam asks: how much is each monthly payment?
The question: Carlos wants to buy a car costing $12 000.
He pays a deposit of $2 000 and takes out a loan from a bank for the remainder. The loan is for 3 years at a nominal annual interest rate of 12%, compounded monthly. Carlos will pay fixed monthly instalments at the end of each month.
(a) Write down the amount Carlos borrows from the bank. [1]
(b) Calculate the amount, correct to the nearest dollar, that Carlos pays each month. [3]
(c) Find the total interest Carlos pays over the 3 years. [2]
Part (a) — Loan amount
Step by step
- Subtract the deposit from the car price.
- Loan = 12 000 − 2 000 = 10 000
- Carlos borrows $10 000. This is a write-down [1] — no TVM needed.
Final answer
Loan amount = $10 000
Part (b) — Monthly payment
Step by step
- Set up the TVM solver: N = 36 (3 years × 12 months), I% = 12, PV = 10 000, FV = 0, P/Y = 12, C/Y = 12.
- PV is positive — Carlos received the loan money. FV = 0 because the loan is fully paid off at the end.
- Solve for PMT → the GDC returns −332.14. The negative sign means money is leaving Carlos each month.
Final answer
Monthly payment = $332 (nearest dollar)
Part (c) — Total interest
Step by step
- Multiply the monthly payment by the number of months: 332 × 36 = 11 952.
- Subtract the original loan amount: 11 952 − 10 000 = 1 952.
Final answer
Total interest = $1 952
Exam Tips:
- Part (a) is always a write-down [1] — just subtract the deposit from the total price. Never use TVM here.
- For part (b): set FV = 0, because the loan is fully repaid at the end. If FV ≠ 0 you will get the wrong PMT.
- Always convert years to months before entering N: 3 years = 36 months.
- For total interest: multiply the monthly payment by the number of months, then subtract the original loan amount.