Using flat rate method, the EMI to repay a loan of ₹ 20,000 in \( 2 \frac{1}{2} \) years at an interest rate of 8% p.a. is:

Question

Self-study helps students to build confidence in learning. It boosts the self-esteem of the learners. Recent surveys suggested that close to 50% of learners were self-taught using internet resources and upskilled themselves.

A student may spend 1 hour to 6 hours in a day in upskilling self. The probability distribution of the number of hours spent by a student is given below:

\[ P(X = x) = \begin{cases} kx^2, & \text{for } x = 1, 2, 3, \\ 2kx, & \text{for } x = 4, 5, 6, \\ 0, & \text{otherwise.} \end{cases} \]

where \( x \) denotes the number of hours. Based on the above information, answer the following questions:
(i) Express the probability distribution given above in the form of a probability distribution table.
(ii) Find the value of \( k \).
(iii)(a) Find the mean number of hours spent by the student.
(iii)(b) Find \( P(1 < X < 6) \).

Answer 1

Step 1: Calculate the total interest: \[{Total Interest} = P \cdot r \cdot t = 20000 \cdot 0.08 \cdot 2.5 = 4000.\] Step 2: Determine the total repayment amount: \[{Total Amount} = 20000 + 4000 = 24000.\] Step 3: Calculate the EMI: \[{Total Months} = 2.5 \times 12 = 30.\]\[{EMI} = \frac{{Total Amount}}{{Total Months}} = \frac{24000}{30} = 800 \, {per month}.\]

Using flat rate method, the EMI to repay a loan of ₹ 20,000 in \( 2 \frac{1}{2} \) years at an interest rate of 8% p.a. is:

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The Correct Option is B

Solution and Explanation

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