The Snowball Effect: Compound Interest
Watch how money grows faster than simple addition. The power of earning interest on interest.
Equation
y = 5000*(1 + 5/100)^x
Graph
Table
| x | y |
|---|---|
| 0 | 5000 |
| 1 | 5250 |
| 2 | 5512.5 |
| 3 | 5788.13 |
| 4 | 6077.53 |
| 5 | 6381.41 |
| 6 | 6700.48 |
| 7 | 7035.5 |
| 8 | 7387.28 |
| 9 | 7756.64 |
| 10 | 8144.47 |
What this lesson covers
What you do
You shape the function y = P*(1 + R/100)^x and watch the graph answer.
Challenges to clear
- Set P = 10000 and R = 10. Year 4 shows 14641 — the first year the amount crosses 14000.
- Same setup: year 2 shows 12100. The snowball accelerates with every year.
- Smaller pot, faster growth. Slide the principal P to 5000.
- Now find the rate that makes Year 2 read 7200. 7200 ÷ 5000 = 1.44, and 1.44 is 1.2 squared.
Check yourself
Why does the graph of Compound Interest curve upwards instead of staying a straight line?
- Because the interest rate R increases every year.
- Because you earn interest on the previous year's interest, not just the principal. — correct
- Because the principal P doubles automatically after two years.
- Because the formula uses a square root for time n.
Think about it
- How does increasing the Rate (R) change the steepness of the growth?
- If you double P, does the whole curve double?