At the end of each year the value of a certain machine has depreciated by $20 \%$ of its value at the beginning of that year. If its initial value was Rs 1250 , find the value at the end of 5 years.

Step 1: Understand Depreciation

The problem states that the machine depreciates by $20\%$ of its value at the beginning of each year. This means its value decreases by $20\%$ annually. We are given the initial value, $V_0 = \text{Rs } 1250$, and the depreciation rate, $r = 20\% = 0.20$.

Step 2: Calculate Value After One Year

After one year, the value of the machine will be its initial value minus the depreciation amount. This can be expressed as $V_0 - V_0 \times r$, which simplifies to $V_0(1 - r)$.

Step 3: General Formula for Depreciation

Since the depreciation occurs annually on the value at the beginning of that year, this is a case of compound depreciation. The value after $n$ years, $V_n$, can be calculated using the formula $V_n = V_0(1 - r)^n$.

Step 4: Substitute Values and Calculate

Now, we substitute the given values into the formula: $V_0 = 1250$, $r = 0.20$, and $n = 5$. First, calculate $(1 - 0.20)^5 = (0.80)^5 = 0.32768$. Then, multiply this by the initial value.

Step 5: Final Calculation

Performing the final multiplication, $1250 \times 0.32768$, we get the value of the machine at the end of 5 years.

More from this chapter

• **Multiple Choice Questions (MCQs)** 13. The sum of money that will produce ₹ 1770 as simple interest in 7(1)/(2) years as 8% at per annum is (a) ₹ 2950 (b) ₹ 3
• 9. Randhir donates ₹ 5000 to a school, the interest of which is to be used for awarding 10 scholarships of equal value every year. If the donation earns an inte
• **Exercise 7.5** 1. In what time ₹ 1600 will amount to ₹ 1760 at rate 5% per annum at simple interest. 2. At what rate of simple interest will a sum double itse
• Out of 20 students in a class, 50% of students are good in science 🧪 find the number of students good in science
• A rocket test model burns fuel at a constant rate. It uses 225 gallons of fuel every 310 of a minute. How many gallons of fuel will it burn in 112?
• **Simple Interest** * P → Principal * R → Rate * T → Time SI = (P × R × T)/(100) A = P + SI **Example** * P = ₹10,000 * R = 10% * T = 2 years * SI = ₹2,000 * Am
• **Very Short Answer Type** 1. Express 75 paise as a percent of ₹ 8. 2. A certain company has 80 employees who are engineers. In this company engineers constitut
• If 3 apples are placed with 6 oranges in an arrangement. How many apples will be placed next to 80 oranges in the same arrangement

All Proportional Reasoning-1 solutions →