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A loan of Rs. 2000 is to be paid back in three equal annual instalments. How much is each instalment, approximately, if the interest is compounded annually at 10% per annum?
- a)Rs. 720
- b)Rs. 750
- c)Rs. 790
- d)Rs. 804
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A loan of Rs. 2000 is to be paid back in three equal annual instalmen...
Solution:
Given:
Loan amount = Rs. 2000
Interest rate = 10% per annum
Number of instalments = 3
To find: Each instalment amount
Explanation:
Since the interest is compounded annually, we can use the formula for the future value of a series of payments:
Future Value = Payment × [(1 + r)^n - 1] / r
Where,
Payment = Each instalment amount
r = Interest rate per period
n = Number of periods
In this case, the loan is to be paid back in three equal annual instalments, so the number of periods (n) is 3.
Using the given values, we can calculate the instalment amount as follows:
Future Value = Rs. 2000
Interest rate = 10% per annum
Number of periods = 3
The formula becomes:
Rs. 2000 = Payment × [(1 + 10%)^3 - 1] / 10%
Simplifying the equation:
Rs. 2000 = Payment × [(1.1)^3 - 1] / 0.1
Rs. 2000 = Payment × [1.331 - 1] / 0.1
Rs. 2000 = Payment × 0.331 / 0.1
Rs. 2000 = Payment × 3.31
To find the value of Payment:
Payment = Rs. 2000 / 3.31
Payment ≈ Rs. 604.83
Since the question asks for the approximate value of each instalment, we can round off the value to the nearest hundredth:
Payment ≈ Rs. 605
Therefore, each instalment is approximately Rs. 605.
The correct answer is not given among the options provided.
Given:
Loan amount = Rs. 2000
Interest rate = 10% per annum
Number of instalments = 3
To find: Each instalment amount
Explanation:
Since the interest is compounded annually, we can use the formula for the future value of a series of payments:
Future Value = Payment × [(1 + r)^n - 1] / r
Where,
Payment = Each instalment amount
r = Interest rate per period
n = Number of periods
In this case, the loan is to be paid back in three equal annual instalments, so the number of periods (n) is 3.
Using the given values, we can calculate the instalment amount as follows:
Future Value = Rs. 2000
Interest rate = 10% per annum
Number of periods = 3
The formula becomes:
Rs. 2000 = Payment × [(1 + 10%)^3 - 1] / 10%
Simplifying the equation:
Rs. 2000 = Payment × [(1.1)^3 - 1] / 0.1
Rs. 2000 = Payment × [1.331 - 1] / 0.1
Rs. 2000 = Payment × 0.331 / 0.1
Rs. 2000 = Payment × 3.31
To find the value of Payment:
Payment = Rs. 2000 / 3.31
Payment ≈ Rs. 604.83
Since the question asks for the approximate value of each instalment, we can round off the value to the nearest hundredth:
Payment ≈ Rs. 605
Therefore, each instalment is approximately Rs. 605.
The correct answer is not given among the options provided.
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Community Answer
A loan of Rs. 2000 is to be paid back in three equal annual instalmen...
Amount to be paid after three years = 2000(1.1)3 = Rs. 2662
Let the annual instalment be Rs. x.
x(1.1)2 + 1.1x + x = Rs. 2662
1.21x + 1.10x + x = Rs. 2662
⇒ x = Rs. 2662/3.31
⇒ x = Rs. 804 (approx.)
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A loan of Rs. 2000 is to be paid back in three equal annual instalments. How much is each instalment, approximately, if the interest is compounded annually at 10% per annum?a)Rs. 720b)Rs. 750c)Rs. 790d)Rs. 804Correct answer is option 'D'. Can you explain this answer?
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