What a repayment actually buys, and the calculator fields that quietly ruin the answer.
Ask how much of the first 1288.60 payment comes off a 200,000 debt.
Guesses cluster around half. It is 288.60, because the interest for that month is 1000. Run the payments and the orange block shrinks across 25 years.
The crossover is payment 163 of 300. Not until then does more of the money go on the debt than on the interest, and that single number does more for financial literacy than the rest of the sub-topic combined.
25 years paid monthly is N = 300. Entering 25 with P/Y = 12 produces a confident, wrong payment, and nothing on the screen looks amiss.
Signs must differ. Money received and money paid go in with opposite signs, which is the other reason an answer comes back negative or absurd. Make them write out all six fields before touching the solver.
| 1. Interest in payment 1 | 0.5% of 200,000 = 1000.00. |
| 2. N for 25 years monthly | 300. |
| 3. Owed after 150 payments | B, about 135,754, well over half. |
1 markN as the number of payments, with the rate matched to the period.
1 markConsistent signs in the finance solver.
1 markTotal interest as total paid minus the amount borrowed.
| They give | What it means |
|---|---|
| 12000 (Q1) | A year of interest rather than a month. |
| 288.60 (Q1) | Gave the part that reduces the debt, which is what is left after the interest. |
| 25 (Q2) | Years, not payments. The single most expensive slip in the sub-topic. |
| A, about 100,000 (Q3) | Assumed the balance falls in a straight line. The figure is the answer. |
| C, about 64,000 (Q3) | Over-corrected. The debt falls slowly at first, not quickly. |
"Why is so much interest?" Because interest is charged on what is still owed, and at the start that is nearly everything. It is not a trick; it is arithmetic.
"Should I overpay?" Mathematically yes, and dramatically so early on, because every pound off the balance removes all the future interest on it. Worth one worked example if there is time.
"What is the difference from an annuity?" The direction of the money. A loan is a lump sum now paid off by instalments; an annuity is instalments bought with a lump sum. Same formula, same screen.
| What is happening | |
|---|---|
| 1 | Guess the first payment split. Reveal. Run to the crossover at 163. |
| 2 | The six calculator fields, written out before anything is typed. |
| 3 | Loan questions: payment, total interest, balance after k payments. |
| 4 | Annuities, as the same thing with the signs swapped. |
| 5 | A real advertised rate, looked up and run. |
Do not let them use the solver before they can say what each field means. The errors here are all data entry, not method.
Do not present this as abstract. It is the sub-topic most likely to matter to them personally, and saying so costs nothing.
Three tiers, ramping the way practice should: the method on its own, then the method inside something real, then a challenge. Set the tier the class in front of you needs rather than one undifferentiated sheet. Answers are given so these can go straight onto a board.
The method on its own, with friendly numbers. Set these first and move on quickly once they are secure.
The same skill inside a real situation, where the first job is working out what is being asked.
Reasoning, working backwards, or spotting an error. These are where the top grades are decided.
Works on a phone. Nothing is loaded from any other site, so it runs behind a school firewall, and nothing a student does is saved or sent anywhere.