Question

A machine worth of Rs. 4,90,740 is depreciated at 15% on its opening value each year. When its value
reduce to Rs. 2,00,000
(a) 5 years 6 months
(b) 5 years 7 months
(c) 5 years 5 months
(d) none

Answer 1

5 years and 5 months

Answer 2

Answer:

(a) 5 years 6 months

Step-by-step explanation:

Given,

• Principal amount, P = Rs. 4,90,740
• Total sum, A = Rs. 2,00,000
• Rate of interest, r = 15%

                                      = 0.15

Since, the rate is depreciating each year with the interest rate of 15% so rate can be taken as -0.15.

So, according to formula of compound interest,

   $A\ =\ P(1+\dfrac{r}{n})^{nt}$

$=>\ 2,00,000\ =\ 4,90,740(1-0.15)^{t}$

$=>\ \dfrac{2,00,000}{4,90,740}\ =\ (0.85)^{t}$

$=>\ 0.4075\ =\ (0.85)^{t}$

$=>\ log(0.4075)\ =\ t.log(0.85)$

$=>\ t\ =\ \dfrac{log(0.4075)}{log(0.85)}$

=> t = 5.52 years

Hence, the time taken by the principal amount to get depreciated to the fixed amount is 5 years 6 months.