Question

the value of machine depreciates at 12.5% per annum . it was purchased 3 years ago. if its present value is 13720 find the original value of the machine 3 years ago

Answer 1

x is original value

x(87.5/100)(87.5/100)(87.5/100)=13720

x=20480

Answer 2

Answer:

The original value of the machine 3 years ago is  Rs 20479.9962 .

Step-by-step explanation:

As the decrease exponential function is given by

$y = a (1-r)^{t}$

Where y is the final value , a is the initial value , r is the rate of interest in the decimal form and t is the time in the years .

As given

The value of machine depreciates at 12.5% per annum . it was purchased 3 years ago. if its present value is 13720 .

y = 13720

12.5% is written in the decimal form

$= \frac{12.5}{100}$

= 0.125

r = 0.125

t = 3 years

Put all the values in the formula

$13720 = a (1-0.125)^{3}$

$13720 = a (0.875)^{3}$

13720 = 0.669922a

$a = \frac{13720}{0.669922}$

a = Rs 20479.9962

Therefore the original value of the machine 3 years ago is  Rs 20479.9962 .