A Machine was purchased for 10,000. Its rate of depreciation is 10% in the first year and 5% per annum afterwards. Find the depreciated value of Machine after 7 years of purchase.

Option b: 6616. Solution: Derivation of Depreciated Machine Value Given: - Initial Cost (V0) = text{Rs. }10,000 - Depreciation rate for 1st year (d1) = 10% - Depreciation rate for subsequent years (d2) = 5% p.a. - Time (t) = 7 years Step 1: Calculate value at the end of the first year (V1) V1 = V0(1 - d1) = 10000(1 - 0.10) = text{Rs. }9,000 Step 2: Calculate value at the end of the remaining 6 years (V7) V7 = V1(1 - d2)^6 V7 = 9000(1 - 0.05)^6 V7 = 9000(0.95)^6 Step 3: Compute the value (0.95)^6 approx 0.73509189 V7 = 9000 x 0.73509189 = text{Rs. }6,615.83 approx text{Rs. }6,616 Hence, Option B is the correct answer.

A Machine was purchased for $10,000$. Its rate of depreciation is $10\%$ in the first year and $5\%$ per annum afterwards. Find the depreciated value of Machine after $7$ years of purchase.

The correct answer is Option b: $6616$. **Derivation of Depreciated Machine Value** Given: - Initial Cost ($V_0$) = $\text{Rs. }10,000$ - Depreciation rate for 1st year ($d_1$) = $10\%$ - Depreciation rate for subsequent years ($d_2$) = $5\%$ p.a. - Time ($t$) = $7$ years **Step 1: Calculate value at the end of the first year ($V_1$)** $$V_1 = V_0(1 - d_1) = 10000(1 - 0.10) = \text{Rs. }9,000$$ **Step 2: Calculate value at the end of the remaining 6 years ($V_7$)** $$V_7 = V_1(1 - d_2)^6$$ $$V_7 = 9000(1 - 0.05)^6$$ $$V_7 = 9000(0.95)^6$$ **Step 3: Compute the value** $$(0.95)^6 \approx 0.73509189$$ $$V_7 = 9000 \times 0.73509189 = \text{Rs. }6,615.83 \approx \text{Rs. }6,616$$ Hence, **Option B** is the correct answer.

Mathematics for FinanceMTP Nov 20Question 1310 of 512

All Questions

A Machine was purchased for $\displaystyle 10,000$ . Its rate of depreciation is $\displaystyle 10\%$ in the first year and $\displaystyle 5\%$ per annum afterwards. Find the depreciated value of Machine after $\displaystyle 7$ years of purchase.

Options

\displaystyle 6606

\displaystyle 6616

\displaystyle 6660

\displaystyle 6661

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — $\displaystyle 6616$

All Options:

A $\displaystyle 6606$
B $\displaystyle 6616$
C $\displaystyle 6660$
D $\displaystyle 6661$

Detailed Solution & Explanation

**Derivation of Depreciated Machine Value** Given: - Initial Cost (

\displaystyle V_0

) =

\displaystyle \text{Rs. }10,000

- Depreciation rate for 1st year (

\displaystyle d_1

) =

\displaystyle 10\%

- Depreciation rate for subsequent years (

\displaystyle d_2

) =

\displaystyle 5\%

p.a. - Time (

\displaystyle t

) =

\displaystyle 7

years **Step 1: Calculate value at the end of the first year (

\displaystyle V_1

)**

V_1 = V_0(1 - d_1) = 10000(1 - 0.10) = \text{Rs. }9,000

**Step 2: Calculate value at the end of the remaining 6 years (

\displaystyle V_7

)**

V_7 = V_1(1 - d_2)^6

V_7 = 9000(1 - 0.05)^6

V_7 = 9000(0.95)^6

**Step 3: Compute the value**

(0.95)^6 \approx 0.73509189

V_7 = 9000 \times 0.73509189 = \text{Rs. }6,615.83 \approx \text{Rs. }6,616

Hence, **Option B** is the correct answer.

Key Concepts to Understand

Depreciation

Allocation of the cost of a tangible fixed asset over its useful life due to wear and tear, efflux of time, or obsolescence.

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

A Machine was purchased for 10,000\displaystyle 10,00010,000. Its rate of depreciation is 10%\displaystyle 10\%10% in the first year and 5%\displaystyle 5\%5% per annum afterwards. Find the depreciated value of Machine after 7\displaystyle 77 years of purchase.