1. Identify the problem: This is a question on compound interest related to installment schemes.
2. Understand the given information:
- Cash price of the computer = ₹75,300
- Cash down payment = ₹25,740
- Interest rate = 20% p.a. compounded half-yearly
- Number of installments = 2 (half-yearly)
3. Calculate the principal amount for installments:
Principal amount for installments = Cash price - Cash down payment = ₹75,300 - ₹25,740 = ₹49,560
4. Calculate the half-yearly interest rate:
Half-yearly interest rate = Annual interest rate / 2 = 20% / 2 = 10%
5. Calculate the amount to be paid after two half-yearly installments using the formula for compound interest:
Amount = P (1 + r/100)^n
Where:
- P = Principal amount = ₹49,560
- r = Half-yearly interest rate = 10%
- n = Number of half-yearly periods = 2
Amount = 49560 (1 + 10/100)² = 49560 (1.1)² = 49560 * 1.21 = ₹60,000 (approximately)
6. Calculate the value of each installment:
Value of each installment = Amount / Number of installments = ₹60,000 / 2 = ₹30,000
7. Calculate the total amount paid under the installment scheme:
Total amount paid = Cash down payment + (Value of each installment * Number of installments) = ₹25,740 + (₹30,000 * 2) = ₹85,740
8. Calculate the total interest paid:
Total interest paid = Total amount paid - Cash price = ₹85,740 - ₹75,300 = ₹10,440
9.Why other options are incorrect: The other options don't accurately reflect the calculation of compound interest over two half-yearly periods. A simple interest calculation would yield a different result. The provided solution accounts for the compounding effect.
Note: There seems to be a discrepancy between the provided correct answer and the calculated value. The calculation above shows a total interest of ₹10,440. The question may have an error in the provided options or the given correct answer.
Important Questions from Installments
A computer is available for Rs. 39,000 on cash payment or Rs. 19,000 as cash payment followed by five monthly instalments of Rs. 4,200 each. What is the rate of interest per annum under the instalment plan?
What is the amount (in Rs.) of debt that will be discharged in 6 equal instalments of Rs. 800 each, if the debt is due in 6 years at 5% per annum?
A sum of Rs. P was borrowed and paid back in two equal yearly instalments, each of Rs. 35,280. If the rate of interest was 5% per annum and interest is compounding annually, then the value of P is ________.
A loan of Rs. 1,50,000 is availed with compound interest rate of 10% per annum for two years compounded annually. It is to be paid in equal yearly installments, and the installment is to be paid at the end of each year. The value of the equal yearly installment is : (Rounded off to two places of decimal)
To buy a car, Sahil borrowed some amount at 10% simple interest rate. He has paid some loan amount but Rs. 1,81,500 is due which he has to pay in 3 years. What will be the annual installment (in Rs.)?
