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 ) = 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) = 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 ≈ 0.73509189 V7 = 9000 × 0.73509189 = Rs. 6,615.83 ≈ 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 of FinanceMCQMTP 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

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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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

Exam Strategy Tip

Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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.

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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.