Question

A new car costs Rs. $360000$.Its price depreciates at the rate of $10$% a year during the first two years and at the rate of $20$% a year thereafter.What will be the price of the car after $3$ years?

Answer 1

Current price of the car, $P_o=Rs360000$
Rate of depreciation, 10% for first 2 years, 20% for the third year
Now, Let price after 2 years= $P$

Thus, $P=P_o(1+\frac{R}{100}{)}^T$

$P=360000(1+\frac{-10}{100}{)}^2$

$P=360000\times \frac{9\times 9}{10\times 10}$

$P=291600$

After the third year, let the price be $P^{\prime }$

$P^{\prime }=P(1+\frac{R^{\prime }}{100}{)}^T$

$P^{\prime }=291600(1+\frac{-20}{100}{)}^1$

$P^{\prime }=\frac{291600\times 80}{100}$

$P^{\prime }=233280$

Thus, the car will cost Rs $233280$ after three years.