Subtracting interest to find original amount
"The Reverse Mistake"
The Mistake in Action
After 3 years at 6% compound interest, an investment is worth £1191.02. Find the original amount.
Wrong: $1191.02 - (0.06 \times 3 \times 1191.02) = 1191.02 - 214.38 = £976.64$
Why It Happens
Students try to "undo" compound interest by calculating and subtracting interest, but this uses simple interest logic.
The Fix
To reverse compound interest, divide by the multiplier raised to the power.
$$P = \frac{\text{Final}}{(1 + r)^n} = \frac{1191.02}{(1.06)^3}$$
$$P = \frac{1191.02}{1.191016} = £1000$$
Key insight: Dividing reverses multiplication, just as the multiplier was applied by multiplication.
Spot the Mistake
Can you identify where this student went wrong?
Find original from £1191.02 after 3 years at 6%
$1191.02 - (0.06 \times 3 \times 1191.02)$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: