Question

A piece of equipment costs a certain factory $Rs.600,000.$ If it in value, $15\%$ the first, $13.5\%$ the next year, $12\%$ the third year and so on. What will be it's a value at the end of $10$ years, all percentages applying to the original cost

• A. $125000$
• B. $115000$
• C. $100000$
• D. $105000$

Answer 1

Answer: (D)

$105000$

The percentage of depreciation at the end of 1st, 2nd and 3rd year are $15\%,13.5\%,12\%$ which are in A.P

with $a=15\%$ and $d=-1.5\%$.

Hence, percentage of depreciation in the 10th year $=a+(10-1)d=15+(10-1)\times (-1.5)=1.5$

Also total value depreciation in 10 year $=15+13.5+12+...+1.5=82.5$

Hence, the value of equipment at the end of 10 years $=100-82.5=17.5$$\%.$

The total cost at the end of 10 years$=Rs.\frac{17.5}{100}\times 600000=Rs.105000$.