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Deepak repays his total loan of ₹1,18,000 by paying every month starting with the first instalment of ₹1000. If he increases the instalment by ₹100 every month. what amount will be paid as the last instalment of loan?
- a)₹4900
- b)₹5400
- c)₹3500
- d)₹4500
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Deepak repays his total loan of 1,18,000 by paying every month startin...
1st instalment = ₹ 1000
2nd instalment = ₹ 1000 + ₹ 100 = ₹ 1100
3rd instalment = ₹ 1100 + ₹ 100 = ₹ 1200 and so on
Let number of instalments = n
∴ 1000 + 1100 + 1200 + ... up to n terms = 118000
⇒ n/2[2x1000+(n-1)100] = 118000
⇒ 100n2 + 1900n – 236000 = 0
⇒ n2 + 19n – 2360 = 0 ⇒ (n + 59)(n – 40) = 0
⇒ n = 40 (∴ n ≠ – 59)
∴ Total no. of instalments = 40
Now, last instalment = 40th instalment
∴ a40 = a + 39d = ₹ 4900
2nd instalment = ₹ 1000 + ₹ 100 = ₹ 1100
3rd instalment = ₹ 1100 + ₹ 100 = ₹ 1200 and so on
Let number of instalments = n
∴ 1000 + 1100 + 1200 + ... up to n terms = 118000
⇒ n/2[2x1000+(n-1)100] = 118000
⇒ 100n2 + 1900n – 236000 = 0
⇒ n2 + 19n – 2360 = 0 ⇒ (n + 59)(n – 40) = 0
⇒ n = 40 (∴ n ≠ – 59)
∴ Total no. of instalments = 40
Now, last instalment = 40th instalment
∴ a40 = a + 39d = ₹ 4900
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Deepak repays his total loan of 1,18,000 by paying every month startin...
The question states that Deepak repays his total loan of INR 1,18,000 by paying every month, starting with the first installment of INR 1000. He increases the installment by INR 100 every month. We need to find out the amount that will be paid as the last installment of the loan.
Let's break down the problem step by step:
Step 1: Calculating the total number of installments
To find out the total number of installments, we need to determine the difference between the first and the last installment.
Let the last installment be 'x'.
The first installment is INR 1000.
The difference between the first and last installment can be calculated using the formula:
Difference = Last Installment - First Installment
Therefore, x - 1000 = (Number of installments - 1) * 100
We know that the loan amount is INR 1,18,000.
So, the total number of installments can be calculated using the formula:
Number of installments = Loan amount / First Installment
Therefore, (x - 1000) = (118000 / 1000 - 1) * 100
(x - 1000) = 117 * 100
x - 1000 = 11700
x = 11700 + 1000
x = 12700
Step 2: Calculating the last installment amount
Now that we have determined the value of 'x' as 12700, which represents the last installment, we can calculate the last installment amount.
Last Installment Amount = First Installment + (Number of installments - 1) * Increase in installment
= 1000 + (12700 - 1) * 100
= 1000 + 12699 * 100
= 1000 + 1269900
= 1270900
Therefore, the amount paid as the last installment of the loan is INR 1270900, which is not one of the given options (a, b, c, d).
Let's break down the problem step by step:
Step 1: Calculating the total number of installments
To find out the total number of installments, we need to determine the difference between the first and the last installment.
Let the last installment be 'x'.
The first installment is INR 1000.
The difference between the first and last installment can be calculated using the formula:
Difference = Last Installment - First Installment
Therefore, x - 1000 = (Number of installments - 1) * 100
We know that the loan amount is INR 1,18,000.
So, the total number of installments can be calculated using the formula:
Number of installments = Loan amount / First Installment
Therefore, (x - 1000) = (118000 / 1000 - 1) * 100
(x - 1000) = 117 * 100
x - 1000 = 11700
x = 11700 + 1000
x = 12700
Step 2: Calculating the last installment amount
Now that we have determined the value of 'x' as 12700, which represents the last installment, we can calculate the last installment amount.
Last Installment Amount = First Installment + (Number of installments - 1) * Increase in installment
= 1000 + (12700 - 1) * 100
= 1000 + 12699 * 100
= 1000 + 1269900
= 1270900
Therefore, the amount paid as the last installment of the loan is INR 1270900, which is not one of the given options (a, b, c, d).
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Deepak repays his total loan of 1,18,000 by paying every month starting with the first instalment of 1000. If he increases the instalment by 100 every month. what amount will be paid as the last instalment of loan?a)4900b)5400c)3500d)4500Correct answer is option 'A'. Can you explain this answer?
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