The real value question that is in the guide and almost never taught.
Ask what 1000 at 5% is worth after ten years, then ask what it BUYS.
They will get 1628.89 and stop, because that is where every textbook stops. The third line on the chart is 1212.03, and the guide explicitly asks for the real value of an investment given an inflation rate.
Then set interest and inflation both to 5% and ask what happened. The number grew 63% and bought nothing extra. That is the moment this sub-topic becomes about something.
Yearly to monthly gains 18.12 on 1000. Monthly to daily gains 1.65. Nothing ever beats 1648.72, and students who expect frequency to matter enormously are surprised by how little it buys.
It is also the only honest answer to “why not compound every second”, and it quietly introduces a limit without naming one.
| 1. 1000 at 5% for 10 years | 1000 × 1.05¹⁰ = 1628.89. |
| 2. 60,000 baht depreciating 15% for 5 years | 60000 × 0.85⁵ = 26,622.32. |
| 3. 5% interest, 5% inflation | B. It buys exactly what it did at the start. |
1 markCorrect k and n. Monthly for ten years is k = 12, n = 10.
1 markThe multiplier for depreciation: 0.85, never −15.
1 markDividing by the inflation factor when real value is asked for, and saying what it means.
| They give | What it means |
|---|---|
| 1500 (Q1) | Simple interest. Worth keeping, because the comparison is the point of the sub-topic. |
| 1647.01 (Q1) | Compounded monthly when the question said yearly. A reading error, and a common one under time pressure. |
| 5000 (Q2) | Took 15% of the original five times. Straight-line depreciation, which is a different model. |
| 11125.89 (Q2) | Gave the loss rather than the remaining value. |
| A (Q3) | The headline trap, and the reason the page exists. The number did grow 63%; it bought nothing more. |
"Is my bank account compound?" Yes, and usually monthly. Worth getting them to find a real rate and run it; it is the most immediately useful thing in Topic 1.
"Why divide by the inflation factor?" Because prices went up by that factor. You are converting future money into today's money, which is the only way to compare the two.
"Is 5% minus 3% not 2%?" Nearly, and it is 1.94%. The rates are ratios, so they divide rather than subtract. The difference is small here and grows with the rates.
| What is happening | |
|---|---|
| 1 | Predict the ten year value. Then show the real value line. |
| 2 | The formula, with k and n named carefully on three examples. |
| 3 | Compounding frequency, and where it stops mattering. |
| 4 | Depreciation as the same formula with a multiplier under 1. |
| 5 | Real value, including the 5% against 5% case. |
Do not present depreciation as a separate formula. It is the same one, and teaching it twice doubles what can be forgotten.
Do not leave real value out because time is short. It is in the guide, it is examinable, and it is the only part students will still use at thirty.
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.