Question

For the depreciation of machinery, relation between Principal (P) and Amount (A) is ----.

a) P < A b) P = A c) P > A​

Answer 1

Given :- For the depreciation of machinery, relation between Principal (P) and Amount (A) is ----.

a) P < A

b) P = A

c) P > A

Answer :- c) P > A

Explantion :-

when rate of machinery is decreased let x % every year, then, amount after let 1 year, or t years will be less than principal => (P > A).

• A = P[1 - (R/100)]^T

if rate of machinery is increased let x % every year, then, amount after let 1 year, or t years will be more than principal . => (P < A) .

• A = P[1 + (R/100)]^T

if no change in rate of machinery => P = A .

therefore, For the depreciation of machinery, relation between Principal (P) and Amount (A) is (c) P > A .

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Answer 2

Given : For the depreciation of machinery,

To Find :  relation between Principal (P) and Amount A  

a) P < A b) P = A c) P > A​

Solution:

relation between Principal (P) and Amount A  

A = P ( 1 + r/100)ⁿ

where P is principal

A = amount after n years

r = rate of change

r +ve  for appreciation

r = - ve for depreciation

r = 0  for no change

r +ve  for appreciation

A = P ( 1 + r/100)ⁿ

1 + r/100 >  1   => ( 1 + r/100)ⁿ > 1

Hence A  > P

r -ve  for depreciation

A = P ( 1 + r/100)ⁿ

1 + r/100 <   1   => ( 1 + r/100)ⁿ <  1

Hence  A  <   P

=> P > A

for r = 0

A = P (1)ⁿ = P

Hence For the depreciation of machinery, relation between Principal (P) and Amount is P > A

Depreciation mean a reduction in the value of an asset overtime.

It is a non-cash expense that reduces the price of an asset.

As time passes, the asset losses it's value known as "Depreciation".

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