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John borrowed Rs.2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal installments, the first after one year and the second after another year. The first installment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each installment, in Rs., is
(2018)
  • a)
    121000
  • b)
    122000
  • c)
    123000
  • d)
    124000
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
John borrowed Rs.2,10,000 from a bank at an interest rate of 10% per a...
Let each installment be Rs. x.
Equating the present value of both the installments to the money borrowed,
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Most Upvoted Answer
John borrowed Rs.2,10,000 from a bank at an interest rate of 10% per a...
Given:
- Principal amount borrowed by John = Rs. 2,10,000
- Interest rate = 10% per annum
- Compounding period = Annually
- Loan repaid in two equal installments

To find:
- The amount of each installment

Solution:
Let's calculate the interest for the first year:

Interest for the first year = Principal * Rate of interest
= 2,10,000 * 10/100
= Rs. 21,000

Now, let's calculate the remaining principal amount after the first installment:

Remaining principal amount = Principal - First installment
= 2,10,000 - 21,000
= Rs. 1,89,000

Since the loan is compounded annually, the remaining principal amount after one year will accumulate interest for the second year.

Interest for the second year = Remaining principal amount * Rate of interest
= 1,89,000 * 10/100
= Rs. 18,900

Now, let's calculate the second installment:

Second installment = Remaining principal amount + Interest for the second year
= 1,89,000 + 18,900
= Rs. 2,07,900

Since both installments are equal, let's calculate the amount of each installment:

Amount of each installment = (First installment + Second installment) / 2
= (21,000 + 2,07,900) / 2
= 2,28,900 / 2
= Rs. 1,14,450

Therefore, each installment is Rs. 1,14,450.

Answer:
The amount of each installment is Rs. 1,14,450. (Option A)
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John borrowed Rs.2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal installments, the first after one year and the second after another year. The first installment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each installment, in Rs., is(2018)a)121000b)122000c)123000d)124000Correct answer is option 'A'. Can you explain this answer?
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