Question

A scooter was bought at $Rs.42,000$. Its value depreciated at the rate of $8\% $ per annum. Find its value after one year.

Answer 1

Hint: Use formula of compound interest $A = P{\left( {1 - \frac{R}{{100}}} \right)^n}$.Compound interest is interest earned in a single year in addition to principal sum.

We have, $P = $ initial principal balance$ = Rs.42,000$
$R = $ Rate of depreciation $ = 8\% $ per annum
Value of scooter after $n$ years$ = P{\left( {1 - \frac{R}{{100}}} \right)^n}$
Value of scooter after $1$ year$ = P{\left( {1 - \frac{R}{{100}}} \right)^1}$
$
   \Rightarrow Rs.42,000\left( {1 - \frac{8}{{100}}} \right) \\
   \Rightarrow Rs.42,000 \times \frac{{92}}{{100}} \\
   \Rightarrow Rs.38640 \\
$
So, the value of a scooter after one year is $Rs.38640$.

Note: whenever we come to these types of problems if the rate of interest is annual and the interest is compounded annually then in such cases we use formula of compound interest and remember for rate of depreciation use negative sign in formula.