What a repayment actually does, and why the balance falls so slowly at the start.
Four quick ones from earlier work. Try each on paper before you open the answer; a slip here shows you what to watch for later in the lesson.
9 ÷ 12 = 0.75%. The annual rate is shared across 12 months. Using 9% as if it were a monthly rate is the slip that makes every later number absurd.
5000 × 1.04³ = 5624.32. Multiply by 1.04 three times, not by 1.12: each year’s interest is earned on the new total.
1200 ÷ 1500 = 0.8, so 80%. Part divided by whole, then convert: the whole here is the payment, not the debt.
24 × 380 = 9120 paid in total, and 9120 − 8000 = 1120 of interest. Two steps: the total paid is not the interest.
Predict first. The payment is the same every month, and the title tells you payment 1 is mostly interest. Before you press Run: when do you think the colours swap, so that more of the payment comes off the debt than goes on interest? Before the halfway point (payment 150 of 300), at it, or after it? Decide first, and give a reason.
Now run the payments and watch the bar and the payment number. Where do the colours swap? Compare that with where you expected them to swap, and see what that tells you about how interest is charged.
200,000 borrowed at 6% a year, repaid monthly over 25 years. The payment is the same 1288.60 every month. Run the payments and watch what it is spent on.
The payment never changes. What it buys does.
Each month, interest is charged on what is still owed, and whatever is left of your payment comes off the debt. Early on the debt is huge, so the interest is huge and almost nothing comes off. As the balance falls, the interest falls with it and the payment starts to bite.
Half the term is not half the debt. After 150 payments of 300 you still owe 135,754 of the 200,000. The total repaid over 25 years is about 386,580, so the interest alone is 186,580, nearly the size of the loan itself.
A loan is a lump sum now, paid off by instalments. An annuity is instalments now, bought with a lump sum. Same formula, same calculator screen, and the only thing that changes is which quantity you are solving for. In the finance solver, money coming to you and money going from you must have opposite signs, which is the single commonest reason an answer comes out negative or absurd.
| Field | Means | Here |
|---|---|---|
| N | number of payments | 300 |
| I% | annual rate | 6 |
| PV | present value | 200000 |
| PMT | payment | −1288.60 |
| FV | future value | 0 |
| P/Y, C/Y | payments and compounds a year | 12, 12 |
N is the number of payments, not the number of years. 25 years paid monthly is N = 300. Putting 25 in N with P/Y = 12 is the error that produces a wildly wrong payment and still looks like a number.
A graduate borrows 400,000 baht for a car at 7% a year, repaid monthly over 5 years.
Find the monthly payment, the total interest, and how much of payment 1 actually reduces the debt.
A loan question is a finance solver question followed by one extra step. The payment comes from the solver; the split between interest and principal comes from the amortisation screen.
When you may use it. Applications. A calculator is allowed in every paper.
The mark people lose. Payment 1 is mostly interest. Students expect roughly half and half. Check the first payment against the total and the shape of the whole loan becomes obvious, which is the actual teaching point.
The same method on a new loan. The first three steps are written out with a reason each; the last one is yours. Cover the reasons and see if you can say them first.
A loan of 90000 at 8.4% a year is repaid by equal monthly payments over 3 years. Find the total interest paid.
Your answer. Type the total interest, to the nearest whole number.
One question that tells you whether the main idea has landed. Each wrong option is a different common slip, so the reply tells you which one you made.
Two loans borrow the same amount at the same annual rate. Loan A is repaid monthly over 15 years and loan B monthly over 30 years. Which statement is correct?
A family wants to borrow 250000 at 5.4% a year, repaid monthly over 20 years. They can afford at most 1700 a month. The calculator is set up with N = 240, I% = 5.4, PV = 250000, FV = 0 and P/Y = C/Y = 12.
Find the monthly payment, to 2 decimal places. Then decide whether the family can afford the loan.
1. A loan of 150,000 baht at 4.8% a year is repaid monthly over 15 years. Find the interest in the first payment.
2. An annuity is to pay out 2000 baht at the end of every month for 10 years. The fund earns 3.6% a year, compounded monthly. How much must be invested now? Give your answer to 2 decimal places.
3. A loan of 120,000 baht at 7.2% a year is repaid monthly over 20 years. After 120 of the 240 payments, the amount still owed is about:
N as the number of payments, and the rate matched to the payment period.
Consistent signs in the finance solver, so money in and money out differ.
Answering the question asked: total interest is total paid minus the amount borrowed, which is two steps, not one.
What if the family on the page (200000 at 6%, monthly, 25 years, payment 1288.60) paid 1500 a month instead? The loan would clear sooner. Roughly how many payments would it need, and how much interest would they save? Predict first, then check on the calculator by solving for N.
Solve for N with PV = 200000, PMT = −1500, FV = 0, I% = 6. Compare the total paid with the 386580 on the page. Before you solve, ask: the extra money goes straight onto the debt, and a smaller debt is charged less interest. So is the saving bigger or smaller than you would first guess?
Four steps, each one a little harder than the last. Every step is a piece of the exam question at the end, so by the top you have already done each part once.
Step 1 of 4: set up the solver. A loan is repaid by equal monthly payments over 4 years. The interest rate is 7.2% per annum, compounded monthly. Which finance-solver entries are right?
Step 2 of 4: find the payment. A loan of 12000 is taken on those terms: 4 years, monthly payments, 7.2% per annum compounded monthly. Find the monthly payment, to 2 decimal places.
Step 3 of 4: find the total interest. For the same loan of 12000, find the total amount of interest paid over the 4 years, to the nearest whole number.
Step 4 of 4: set up what is still owed. For the same loan of 12000, which calculation gives the amount still owed immediately after the 12th payment?
Written for this site in the style of the real papers. Do it on paper first, as you would in the exam, and show your working: most of the marks are for method. Give answers to 3 significant figures unless the question says otherwise. Then check each part below.
Paper 1 style · calculator (GDC) allowed · 7 marks · about 8 minutes
Amara borrows 18000 to buy a car. The loan is to be repaid with equal monthly payments over 5 years. The interest rate is 6.6% per annum, compounded monthly.
(a) Find the amount of each monthly payment. Give your answer correct to two decimal places. [3]
(b) Find the total amount of interest Amara will pay over the 5 years. Give your answer to the nearest whole number. [2]
(c) After 2 years Amara decides to repay the rest of the loan in a single payment. Find the amount she still owes immediately after her 24th monthly payment. Give your answer to the nearest whole number. [2]
Check (a). Type your monthly payment, to 2 decimal places.
Check (b). Type the total interest, to the nearest whole number.
Check (c). Type the amount still owed after 24 payments, to the nearest whole number.
These three are deliberately not all about this page. In an examination the hardest step is deciding which method applies, and questions that arrive straight after the method never make you decide. Answer from memory before you reveal anything.
Come back to these in a week, and again in a month.
Which method?
A ball bounces for ever, rebounding to 0.8 each time. Does it travel a finite distance?
Which method?
Find the modulus of 3 + 4i.
Which method?
200000 at 6% a year, monthly, over 25 years. How many payments?
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