An investment grew at a compound annual growth rate (CAGR) of 10% and was worth Rs. 66,550 at the end of 3 years. The amount invested at the start was
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs. 50,000
With a CAGR of 10%, the value is multiplied by 1.1 every year, so
\( \text{EV} = \text{SV} \times (1.1)^3 \)
\( (1.1)^3 = 1.331 \)
\( \displaystyle \text{SV} = \frac{66550}{1.331} = 50000 \)
Why the other options are incorrect
Option (2) Rs. 60,500 — Incorrect. This divides by 1.1 only once, which goes back just one year.
Option (3) Rs. 51,192.31 — Incorrect. This divides by 1.3, treating the growth as simple growth of 10% a year.
Option (4) Rs. 46,585 — Incorrect. This takes 30% off the final value; growth must be undone by division, not by subtraction.