Question

in how many years would an asset amounting to Rs 12500 be reduced to the value of Rs 64000. if the compound depreciation is charged 20% p.a.​

Answer 1

To calculate the number of years it would take for an asset to depreciate from Rs 12500 to Rs 64000 at a compound depreciation rate of 20% per annum, we can use the following formula:

A = P(1 - r/n)^(nt)

where,

A = final amount (Rs 64000)

P = initial amount (Rs 12500)

r = annual interest rate (20%)

n = number of times the interest is compounded per year (1)

t = time (number of years)

By substituting the given values in the formula, we get:

64000 = 12500(1 - 0.2/1)^(1t)

Simplifying the equation, we get:

(1 - 0.2)^(t) = 64000/12500

0.8^(t) = 5.12

Taking the logarithm of both sides, we get:

t*log(0.8) = log(5.12)

t = log(5.12)/log(0.8)

t = 7.5 years (approx.)

Therefore, it would take approximately 7.5 years for the asset to depreciate from Rs 12500 to Rs 64000 at a compound depreciation rate of 20% per annum.