A mobile phone is available for ₹25,000 or ₹5,200 down payment, followed by 4 equal monthly installments. If the rate of interest is 25% p.a. simple interest, calculate the amount of each installment.
(a) ₹5,020
(b) ₹5,200
(c) ₹5,362
(d) ₹5,355
Answer (2)
To find the amount of each monthly installment, we will first determine the loan amount, then calculate the simple interest for the entire loan term, and finally find the monthly installment amount.
Step 1: Determine the loan amount
The total cost of the mobile phone is ₹25,000. The student makes a down payment of ₹5,200.
Thus, the loan amount is: Loan Amount = ₹25 , 000 − ₹5 , 200 = ₹19 , 800
Step 2: Calculate the simple interest
The rate of interest is 25% per annum (p.a.), and since the installments are over 4 months, we need to calculate the interest for this period. We convert the annual interest rate to a monthly interest rate:
1 year = 12 months, which means the monthly rate of interest is: \text{Monthly Interest Rate} = \frac{25\%}{12} = \frac{25}{100 \times 12} = \frac{1}{48}\
The interest for 4 months can be calculated using the formula for simple interest: Interest = Principal × Rate × Time Here:
Principal = Loan Amount = ₹19,800
Rate per month = 48 1
Time = 4 months
Plug these values into the simple interest formula: I n t eres t = 19 , 800 × 48 1 × 4 = ₹16 , 50
Step 3: Calculate the total amount to be repaid
The total repayment amount (Principal + Interest) over the 4 months is: Total Repayment = 19 , 800 + 1 , 650 = ₹21 , 450
Step 4: Calculate each monthly installment
Since there are 4 equal monthly installments, the amount of each installment is: Installment = 4 21 , 450 = ₹5 , 362.50
However, the options provided in the question do not offer ₹5,362.50. Thus, assuming rounding requirements or calculation correctness, the closest correct option in the choices provided is
Option (c) ₹5,362 .
Therefore, the amount of each installment rounded to the nearest rupee is ₹5,362 .
The monthly installment for the mobile phone, after calculating the down payment, simple interest, and total repayment, is approximately ₹5,362. The chosen option from the list is (c) ₹5,362.
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