Log in

Sign up
You said:
A machine costing  ₹ 2,00,000 depreciates at a constant rate of 10%. What is value of machine after 5 years?

Select one:
 ₹  86,093.44
₹ 1,02,643.77
 ₹. 1,18,098
₹ 1,31,816

The problem requires us to calculate the value of a machine after 5 years, given that it depreciates at a constant rate of 10% per year. 

### Step-by-Step Solution:

1. **Initial Value (P):** ₹ 2,00,000
2. **Depreciation Rate (r):** 10% per year
3. **Number of Years (n):** 5

The value of the machine after \(n\) years can be calculated using the formula:

\[
V_n = P \times (1 - r)^n
\]

Substitute the given values:

\[
V_5 = 2,00,000 \times (1 - 0.10)^5
\]

Simplify:

\[
V_5 = 2,00,000 \times (0.90)^5
\]

Calculate \( (0.90)^5 \):

\[
(0.90)^5 \approx 0.59049
\]

Now, calculate the final value:

\[
V_5 = 2,00,000 \times 0.59049 \approx 1,18,098
\]

### Final Answer:
The value of the machine after 5 years is approximately **₹ 1,18,098**.

### Correct Option:
The correct option is **₹ 1,18,098**.

Would you like more details or have any questions?

---

**Related Questions:**
1. What would be the value of the machine after 3 years with the same depreciation rate?
2. If the depreciation rate was 12%, what would the value of the machine be after 5 years?
3. How long would it take for the machine's value to drop below ₹ 1,00,000 with a 10% depreciation rate?
4. What is the total depreciation amount over 5 years?
5. What is the annual depreciation amount for the first year?

**Tip:** When dealing with constant depreciation, the value decreases exponentially over time. This makes it important to account for compounding when estimating long-term values.

Learn how to calculate the value of a machine after 5 years with a constant depreciation rate of 10% per year. Understand the exponential decay process and apply the formula to find the final value. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation