Question

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

Answer 1

let the principal 3 years ago be P
R%=12.5= 125/10
time= 3 yrs
So P[1-(125/1000)]^3=13720
P[7/8]^3= 13720
P= (13720×512)÷343
P= 40×512= 20480

so the original price of the machine was 20480

Answer 2

Let Principal (P) = ₹ P
Rate of interest (R) = Depreciation = 12.5% p.a
Time (n) = 3 years
Amount = ₹ 13720

$Amount = P {(1 - \frac{R}{100} )}^{n} \\ \\ 13720 = P {(1 - \frac{12.5}{100} )}^{3} \\ \\ 13720 = P {(1 - \frac{125}{1000} )}^{3} \\ \\ 13720 = P {(1 - \frac{1}{8} )}^{3} \\ \\ 13720 = P {( \frac{8 - 1}{8} )}^{3} \\ \\ 13720 = P {( \frac{7}{8}) }^{3} \\ \\ 13720 = \frac{343}{512} P \\ \\ 13720 \times \frac{512}{343} = P \\ \\ 20480 = P$

Hence, the original value of the machine 3 years ago was ₹ 20480.