The CI Formula: A = P(1+r/100)^n
Watch how repeated interest builds into a single powerful formula.
Equation
y = 1000*(1 + 5/100)^x
Graph
Table
| x | y |
|---|---|
| 0 | 1000 |
| 1 | 1050 |
| 2 | 1102.5 |
| 3 | 1157.63 |
| 4 | 1215.51 |
What this lesson covers
What you do
You shape the function y = 1000*(1 + r/100)^x and watch the graph answer.
Challenges to clear
- Set r = 10: after 2 years, A = 1000 × (1.1)² = 1210.
- Year 4: 1000 × (1.1)⁴ = 1464.10 — the formula compounds automatically.
- The principal is yours to set now. Slide P to 2000.
- Now the rate: Year 2 must read 2880. That is 2000 × 1.2², so the rate is 20%.
Check yourself
In the formula A = P(1 + r/100)^n, what does the exponent 'n' represent?
Why do we calculate (1 + r/100) first before raising it to the power n?
- The rate of interest per annum
- The number of years (time period) — correct
- The total interest earned
- The principal amount invested
- Because we need to find the Simple Interest first.
- To create a single multiplier that includes both the principal and one year's interest. — correct
- Because the formula requires us to add 1 to the rate.
- To convert the percentage into a decimal.
Think about it
- P = 1000, r = 10%, n = 2 years. What Amount does A = P(1 + r/100)^n give?