Question

A car loses value at a rate of $27$% each year. How long will it take for its value to halve?

Answer 1

Formula of compounding can be used here.

Let the price of car be $x$

We know that compound formula $\Rightarrow S=P(1+\frac{R}{100}{)}^n$

$\Rightarrow \frac{x}{2}=x(1-\frac{27}{100}{)}^n$

Here we used ${}^{\prime }{-}^{\prime }$ sign because the amount is decreasing

$\Rightarrow \frac{1}{2}=(1-0.27{)}^n$

$\Rightarrow \frac{1}{2}=(0.73{)}^n$

$\Rightarrow n\approx 2.2years$