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A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.723 more, if the interest was payable half yearly than if it was payable annually. The sum is ____
- a)Rs. 20000
- b)Rs. 15000
- c)Rs. 30000
- d)Rs. 45000
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A sum of money lent at compound interest for 2 years at 20% per annum ...
sum – Rs.x
C.I. compounded half yearly = (4641/10000)x
C.I. compounded annually = (11/25)x
(4641/10000)x – (11/25)x = 723
x = 30000
Most Upvoted Answer
A sum of money lent at compound interest for 2 years at 20% per annum ...
Compound Interest Problem
Given:
- Time period = 2 years
- Annual interest rate = 20%
- Interest payable half yearly
- Difference in interest = Rs. 723
To find: The principal amount
Solution:
Let the principal amount be P.
We know that the formula for compound interest is:
A = P(1 + r/n)^(nt)
Where,
A is the amount
P is the principal amount
r is the rate of interest
t is the time period in years
n is the number of times the interest is compounded per year
Annual Interest:
If the interest is payable annually, then the formula becomes:
A = P(1 + r)^t
= P(1 + 0.20)^2
= P(1.44)
= 1.44P
Half Yearly Interest:
If the interest is payable half yearly, then the formula becomes:
A = P(1 + r/2)^(2t)
= P(1 + 0.10)^4
= P(1.4641)
= 1.4641P
Difference in Interest:
The difference in interest between the two cases is Rs. 723.
Therefore,
1.4641P - 1.44P = 723
0.0241P = 723
P = Rs. 30000
Therefore, the principal amount is Rs. 30000.
Answer: Option (c) Rs. 30000
Given:
- Time period = 2 years
- Annual interest rate = 20%
- Interest payable half yearly
- Difference in interest = Rs. 723
To find: The principal amount
Solution:
Let the principal amount be P.
We know that the formula for compound interest is:
A = P(1 + r/n)^(nt)
Where,
A is the amount
P is the principal amount
r is the rate of interest
t is the time period in years
n is the number of times the interest is compounded per year
Annual Interest:
If the interest is payable annually, then the formula becomes:
A = P(1 + r)^t
= P(1 + 0.20)^2
= P(1.44)
= 1.44P
Half Yearly Interest:
If the interest is payable half yearly, then the formula becomes:
A = P(1 + r/2)^(2t)
= P(1 + 0.10)^4
= P(1.4641)
= 1.4641P
Difference in Interest:
The difference in interest between the two cases is Rs. 723.
Therefore,
1.4641P - 1.44P = 723
0.0241P = 723
P = Rs. 30000
Therefore, the principal amount is Rs. 30000.
Answer: Option (c) Rs. 30000
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A sum of money lent at compound interest for 2 years at 20% per annum ...
C 30000
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A sum of money lent at compound interest for 2 years at 20% per annum would fetch Rs.723 more, if the interest was payable half yearly than if it was payable annually. The sum is ____a)Rs. 20000b)Rs. 15000c)Rs. 30000d)Rs. 45000e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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