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A sum of money is lent for 2 years at 10% p.a. compound interest. It yields Rs 8.81 more when compounded semi-annually than compounded annually. What is the sum lent?
- a)1000
- b)1200
- c)1400
- d)1600
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A sum of money is lent for 2 years at 10% p.a. compound interest. It y...
8.81 = p*(1+5/100)4 – p*(1+10/100)2
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A sum of money is lent for 2 years at 10% p.a. compound interest. It y...
Given:
- Principal amount = ?
- Time period = 2 years
- Rate of interest = 10%
- Difference in interest when compounded semi-annually and annually = Rs 8.81
To find: Principal amount
Solution:
Let the principal amount be P.
When the interest is compounded annually, the amount after 2 years can be calculated using the formula:
A = P(1 + R/100)^n
where A is the amount, R is the rate of interest, and n is the time period.
So, when interest is compounded annually, the amount after 2 years is:
A1 = P(1 + 10/100)^2
A1 = P(1.1)^2
A1 = 1.21P
When interest is compounded semi-annually, the amount after 2 years can be calculated using the formula:
A = P(1 + R/2/100)^(2*n)
where A is the amount, R is the rate of interest, and n is the number of compounding periods per year.
So, when interest is compounded semi-annually, the amount after 2 years is:
A2 = P(1 + 5/100)^4
A2 = P(1.05)^4
A2 = 1.21550625P
The difference in interest between compounding annually and semi-annually is:
A2 - A1 = Rs 8.81
Substituting the values of A1 and A2, we get:
1.21550625P - 1.21P = 8.81
0.00550625P = 8.81
P = 8.81/0.00550625
P = Rs 1600
Therefore, the principal amount lent was Rs 1600.
Answer: Option (d) 1600.
- Principal amount = ?
- Time period = 2 years
- Rate of interest = 10%
- Difference in interest when compounded semi-annually and annually = Rs 8.81
To find: Principal amount
Solution:
Let the principal amount be P.
When the interest is compounded annually, the amount after 2 years can be calculated using the formula:
A = P(1 + R/100)^n
where A is the amount, R is the rate of interest, and n is the time period.
So, when interest is compounded annually, the amount after 2 years is:
A1 = P(1 + 10/100)^2
A1 = P(1.1)^2
A1 = 1.21P
When interest is compounded semi-annually, the amount after 2 years can be calculated using the formula:
A = P(1 + R/2/100)^(2*n)
where A is the amount, R is the rate of interest, and n is the number of compounding periods per year.
So, when interest is compounded semi-annually, the amount after 2 years is:
A2 = P(1 + 5/100)^4
A2 = P(1.05)^4
A2 = 1.21550625P
The difference in interest between compounding annually and semi-annually is:
A2 - A1 = Rs 8.81
Substituting the values of A1 and A2, we get:
1.21550625P - 1.21P = 8.81
0.00550625P = 8.81
P = 8.81/0.00550625
P = Rs 1600
Therefore, the principal amount lent was Rs 1600.
Answer: Option (d) 1600.
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A sum of money is lent for 2 years at 10% p.a. compound interest. It y...
A sum of money is lent for 2 years at 10% p.a. compound interest. It yields Rs 8.81 more when compounded
semi-annually than compounded annually. What is the sum lent?
semi-annually than compounded annually. What is the sum lent?
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A sum of money is lent for 2 years at 10% p.a. compound interest. It yields Rs 8.81 more when compounded semi-annually than compounded annually. What is the sum lent?a)1000b)1200c)1400d)1600e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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