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A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment is
- a)Rs.127
- b)Rs.121
- c)Rs.210
- d)Rs.225
Correct answer is option 'B'. Can you explain this answer?
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A sum of Rs. 210 was taken as a loan. This is to be paid back in two ...
Let x be the value of installment.
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Principal = Present value of x for 1 year + Present value of x for 2 years
Most Upvoted Answer
A sum of Rs. 210 was taken as a loan. This is to be paid back in two ...
Given:
- Loan amount = Rs. 210
- Loan to be repaid in two equal installments
- Rate of interest = 10% per annum compounded annually
To Find:
Value of each installment
Solution:
We can solve this problem using the concept of present value of an annuity.
Step 1: Calculate the present value of the loan amount
The present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. In this case, the future sum of money is the loan amount of Rs. 210, and the specified rate of return is 10% per annum compounded annually.
The formula to calculate the present value of an amount compounded annually is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.
In this case, FV = Rs. 210, r = 10% = 0.1, and n = 2 (as there are two installments).
Substituting the values into the formula, we get:
PV = 210 / (1 + 0.1)^2
PV = 210 / (1.1)^2
PV = 210 / 1.21
PV = 173.55
Therefore, the present value of the loan amount is Rs. 173.55.
Step 2: Calculate the value of each installment
Since the loan is to be repaid in two equal installments, the value of each installment can be calculated by dividing the present value of the loan amount by the number of installments.
Value of each installment = PV / number of installments
Value of each installment = 173.55 / 2
Value of each installment = Rs. 86.775
Rounding off to the nearest rupee, the value of each installment is Rs. 87.
Conclusion:
The value of each installment is Rs. 87, which corresponds to option B.
- Loan amount = Rs. 210
- Loan to be repaid in two equal installments
- Rate of interest = 10% per annum compounded annually
To Find:
Value of each installment
Solution:
We can solve this problem using the concept of present value of an annuity.
Step 1: Calculate the present value of the loan amount
The present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. In this case, the future sum of money is the loan amount of Rs. 210, and the specified rate of return is 10% per annum compounded annually.
The formula to calculate the present value of an amount compounded annually is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.
In this case, FV = Rs. 210, r = 10% = 0.1, and n = 2 (as there are two installments).
Substituting the values into the formula, we get:
PV = 210 / (1 + 0.1)^2
PV = 210 / (1.1)^2
PV = 210 / 1.21
PV = 173.55
Therefore, the present value of the loan amount is Rs. 173.55.
Step 2: Calculate the value of each installment
Since the loan is to be repaid in two equal installments, the value of each installment can be calculated by dividing the present value of the loan amount by the number of installments.
Value of each installment = PV / number of installments
Value of each installment = 173.55 / 2
Value of each installment = Rs. 86.775
Rounding off to the nearest rupee, the value of each installment is Rs. 87.
Conclusion:
The value of each installment is Rs. 87, which corresponds to option B.
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A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer?
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A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer?.
A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer?.
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A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A sum of Rs. 210 was taken as a loan. This is to be paid back in two equal installments. If the rate of interest be 10% compounded annually, then the value of each installment isa)Rs.127b)Rs.121c)Rs.210d)Rs.225Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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