The Snowball Effect: CI vs SI
Watch how interest earns interest. See why Compound Interest grows faster than Simple Interest over time.
Equation
y = 2000 * ((1 + 8/100)^x - 1) - (2000 * 8 * x) / 100
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | 0 |
| 2 | 12.8 |
| 3 | 39.42 |
| 4 | 80.98 |
| 5 | 138.66 |
| 6 | 213.75 |
| 7 | 307.65 |
| 8 | 421.86 |
| 9 | 558.01 |
| 10 | 717.85 |
What this lesson covers
What you do
You shape the function y = P * ((1 + R/100)^x - 1) - (P * R * x) / 100 and watch the graph answer.
Challenges to clear
- Set P = 5000 and R = 10. After 2 years the snowball gap (CI − SI) is exactly Rs 50.
- By year 3 the gap triples to Rs 155 — interest is earning interest.
- A bigger principal: slide P to 8000.
- Now find the rate where the 2-year gap between compound and simple interest is exactly Rs 20. That gap is P × (R/100)² — small at first, then it runs away.
Check yourself
Why does the gap between Simple Interest and Compound Interest grow wider every year?
- Because Simple Interest stops after year 1.
- Because Compound Interest is calculated on the accumulated amount (Principal + previous interest), so interest earns interest. — correct
- Because the bank charges a penalty on Simple Interest.
- Because Compound Interest uses a higher rate automatically.
Think about it
- If you increase the Rate (R), does the curve get steeper faster?
- If you double the Principal (P), does the Compound Interest double too?