Compound Interest: The Formula in Action
Watch how P, r, and n combine to calculate the final amount using A = P(1 + r/100)^n.
Equation
y = 2000*(1+10/100)^x
Graph
Table
| x | y |
|---|---|
| 0 | 2000 |
| 1 | 2200 |
| 2 | 2420 |
| 3 | 2662 |
| 4 | 2928.2 |
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 = 8000 and r = 5. Read the table at x = 2: the compound amount is 8820.
- Two more years: x = 4 shows 9724.05. The formula compounds by itself.
- New principal: slide P to 6000.
- Now the rate. Year 2 must read 7260 — that is 6000 × 1.1², so the rate is 10%.
Check yourself
In the formula A = P(1 + r/100)^n, what does the term (1 + r/100) represent?
Why do we calculate (1 + r/100)^n instead of multiplying the interest by n?
- The growth factor for one year — correct
- The total interest earned over n years
- The principal amount plus total interest
- The rate of interest per year
- Because interest earns interest in subsequent years — correct
- Because the rate changes every year
- Because simple interest is not applicable
- Because the principal increases every year
Think about it
- A = P(1 + r/100)^n with P = 8000, r = 5, n = 2. What is A?