Question

The value of a machine depreciates every year at the rate of $10\% $ of its value at the beginning of that year. If the present value of the machine is Rs. $729,$ it's worth three years ago was:
A.Rs. $1000$
B.Rs. $750.87$
C.Rs. $800$
D.Rs. $947.70$

Answer 1

Hint: Depreciation is calculated on the basis of taking the purchase or acquisition price of an asset subtracted by the retrieve value divided by the total productive years the asset can be reasonably expected to work in the proper condition to make benefits for the company.

Complete step-by-step answer:
Given that: Machine depreciates at the rate, R $ = 10\% $
                    Present value of the machine, P $ = 729$ Rs.
                   Term, T $ = 3$ years
As we know that,
Amount,
$A = \dfrac{p}{{{{(1 - R/100)}^T}}}$
Substitute all the given values,
$\begin{array}{l}
A = \dfrac{{729}}{{{{(1 - 10/100)}^3}}}\\
A = \dfrac{{729}}{{{{(0.9)}^3}}}\\
A = 1000
\end{array}$
 Thus, $1000$ rupees was the value of the machine three years before.
Therefore, from the given options, option A is the correct answer.
Additional Information: Depreciation is the reduction of the recorded cost of the fixed assets such as buildings, furniture, office equipment, machinery and many more. Depreciation is noted in every company as revenues are recorded with their associated expenses.

Note: This problem can also be solved alternatively by increasing 10% of the present price upto three years and then get the value of machine three years before.