GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
GROW — Interest, decline and successive changes
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with a prediction.
At 10% per year, does the second year add the same amount under simple interest and annual compounding?
Sketch or write an independent attempt before reading on. Test your idea using the model.
Understand
Simple interest adds interest calculated on the original principal. Compounding applies each new rate to the updated amount. Repeated decline also changes the base.
Key Ideas
p = original principal; t = whole years; r = annual rate as a decimal (10% → 0.10).
Annual compounding:
For a decline at decimal rate d, replace the factor by (1 − d). These models assume a constant stated rate and no additional deposits or withdrawals.
Use r = 0.10 for 10%, not r = 10. Successive percentage changes multiply; they are not normally added.
Visualise
Simple and compound growth
Predict first. Change the controls, then compare your reasoning.
| Period | Simple | Compound |
|---|---|---|
| 0 | 1000.00 | 1000.00 |
| 1 | 1100.00 | 1100.00 |
| 2 | 1200.00 | 1210.00 |
| 3 | 1300.00 | 1331.00 |
Each compound period multiplies the current amount by 1.1. Calculations retain full precision between periods.
A shrinking base
Predict first. Change the controls, then compare your reasoning.
| Period | Remaining |
|---|---|
| 0 | 1000.00 |
| 1 | 900.00 |
| 2 | 810.00 |
| 3 | 729.00 |
Each period retains 90% (factor 0.9). Calculations retain full precision between periods.
Successive changes multiply
Predict first. Change the controls, then compare your reasoning.
Overall discount = 44%. Multiply (0.7) × (0.8); the second discount uses 70 as its base.
Method
Convert the annual percentage rate to decimal r. Simple amount: p(1 + rt). Annual compound amount: p(1 + r) raised to t. For decline use a factor below 1; multiply factors for successive changes.
Worked Example
Given
Principal ₹6000, 10% per year, 3 years.
To Find
Simple and annually compounded final amounts
Reasoning
Use decimal rate r = 0.10; keep intermediate values unrounded.
Solution
- Simple: 6000 × (1 + 0.10 × 3) = ₹7800.
- Compound: 6000 × 1.1 × 1.1 × 1.1 = ₹7986.
- Difference: 7986 − 7800 = ₹186.
Result
Compounding gives ₹186 more after 3 years.
AIMS Method
- A — Attempt independently
Estimate and predict first. - I — Investigate the idea
Identify the whole and the percentage base. - M — Make connections
Connect fractions, decimals, bars and multipliers. - S — Scrutinise your reasoning
Check units, bases and the reasonableness of the result.
Think first. Use AI purposefully. Verify always.
Focused Practice
An initial mouse population p changes by +5%, −2%, then −3%. Is the final model above or below p?
Check & Feedback
Name the whole, explain the method and give one check that would catch a wrong percentage base.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 22