To find the value of each instalment, we need to use the concept of equal instalments with simple interest applied individually to each instalment until the total amount is paid. The formula for simple interest is:
\(I = P \times \frac{r \times t}{100}\) where P is the principal, r is the rate of interest, and t is the time period.
- The total amount to be paid after 4 years is ₹1,380, and the simple interest rate is 10% on each instalment.
- Let the value of each instalment be ₹X.
- The four instalments will be paid at the end of 1st, 2nd, 3rd, and 4th years. Each instalment will generate interest for the remaining years until the end of 4 years. Therefore, we have:
- The 1st instalment is paid at the end of the 1st year, generating interest for 3 years.
- The 2nd instalment is paid at the end of the 2nd year, generating interest for 2 years.
- The 3rd instalment is paid at the end of the 3rd year, generating interest for 1 year.
- The 4th instalment is paid at the end of the 4th year, generating interest for 0 years.
- Now, we calculate the total payment at the end of the 4th year, which includes all the principal instalments plus the interest from each instalment:
- Total payment from the 1st instalment = \(X + X \times \frac{10 \times 3}{100} = X + 0.3X\) = \(1.3X\)
- Total payment from the 2nd instalment = \(X + X \times \frac{10 \times 2}{100} = X + 0.2X\) = \(1.2X\)
- Total payment from the 3rd instalment = \(X + X \times \frac{10 \times 1}{100} = X + 0.1X\) = \(1.1X\)
- Total payment from the 4th instalment = \(X\) (since it has no interest)
- Add up all these terms, which equals the total amount to be paid:
- Total amount = \(1.3X + 1.2X + 1.1X + X = 4.6X\)
- According to the given question, the total amount to be paid is ₹1,380. Therefore:
- \(4.6X = 1380\)
- To find the value of X (each instalment):
- \(X = \frac{1380}{4.6} = 300\)
Therefore, the value of each instalment is ₹300. Thus, the correct answer is ₹300.
Similar Questions
- A man has to discharge a debt of ₹15,600 which is due in 3 years at 4% simple interest per annum. If he pays this amount in equal instalments of annual payment, find the amount for annual payment.
- The annual instalment (in) to discharge a debt of ₹8,432 due in 4 years at 16% simple interest per annum is:
- An annual instalment of ₹3,500 will discharge a debt of ₹16,310 due in 4 years at y% simple interest per annum. What is the value of y? [Note: Instalments will be paid at the end of Year 1, Year 2, Year 3 and Year 4.
- The amount of debt that will be discharged by 5 equal monthly instalments of ₹1,845 each, at the rate of 48% simple interest per annum, is:
What equal instalment of annual payment (in) will discharge a debt that is due as ₹624 at the end of 5 years at 2% per annum simple interest?
What annual installment will discharge a debt of ₹5,460 due in 5 years at 10% simple interest per annum?
- A man borrowed money for 2 years and paid back in two equal annual instalments of ₹2,260 at 5% compound interest, compounded annually. What was the sum (in ₹, to the nearest tens) borrowed?
- A loan of ₹2,550 is to be paid back in two equal half-yearly instalments. How much is each instalment if the interest is compounded half-yearly at 8% p.a.?
- What annual instalment will discharge a debt of Rs.3,658 due in four years at 12% simple interest per annum?
- Find the amount of equal annual instalment, which will discharge a debt of Rs.40,376 due in 4 years at the rate of 2% p.a. simple interest.
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)
- A computer is available for ₹75,300 cash or for ₹25,740 cash down payment and two equal half-yearly instalments. If the dealer charges interest at 20% p.a., compounded half-yearly, then the total interest to be paid by a customer who buys it in instalment scheme is:
