The cost of a property appreciates by 10% of the previous month every month. If in end march 2024 it was ₹13.31 lakh, when was it ₹10 lakh?

end-december 2023

The correct answer is Option (2) → end-december 2023

Given:

Final value in March 2024: $A = 13.31$ lakh

Monthly appreciation rate: $r = 10\% = 0.1$

Let the value in month $n$ months before March 2024 be $P$:

Compound formula: $A = P (1 + r)^n$

Substitute $P = 10$ lakh, $A = 13.31$ lakh, $r = 0.1$:

$13.31 = 10 (1.1)^n \Rightarrow (1.1)^n = 1.331$

Check: $1.1^3 = 1.331 \Rightarrow n = 3$ months

Counting backwards from end March 2024:

End March → End Feb → End Jan → End Dec 2023

Value was ₹10 lakh at end-December 2023