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The difference between compound interest compounded every 6 months and simple interest after 2 years is 248.10. The rate of interest is 10 percent. Find the sum
- a)12000
- b)14000
- c)16000
- d)18000
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The difference between compound interest compounded every 6 months and...
Explanation : P*(1+5/100)4 – P – P*(10/100)*2 = 248.10
P = 16000
P = 16000
Most Upvoted Answer
The difference between compound interest compounded every 6 months and...
Explanation : P*(1+5/100)4 – P – P*(10/100)*2 = 248.10
P = 16000
P = 16000
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Community Answer
The difference between compound interest compounded every 6 months and...
Given:
Rate of interest = 10%
Difference between compound interest and simple interest = $248.10
To find: The principal amount (Sum)
Let's assume the principal amount as P.
Calculation:
1. Simple Interest after 2 years:
Simple Interest = (P * R * T) / 100
Where,
P = Principal amount
R = Rate of interest
T = Time period (in years)
Simple Interest = (P * 10 * 2) / 100 = 0.2P
2. Compound Interest compounded every 6 months:
Since the interest is compounded every 6 months, the effective rate of interest for 2 years will be half of the given rate. So, the effective interest rate for compound interest will be 5%.
Compound Interest = P * (1 + R/100)^n - P
Where,
P = Principal amount
R = Rate of interest
n = Number of times interest is compounded per year (in this case, 2 years)
Compound Interest = P * (1 + 5/100)^4 - P = 1.2155P - P = 0.2155P
3. Difference between compound interest and simple interest:
Difference = Compound Interest - Simple Interest
248.10 = 0.2155P - 0.2P
248.10 = 0.0155P
To find P, divide both sides of the equation by 0.0155:
P = 248.10 / 0.0155 = 16000
Therefore, the principal amount (Sum) is $16,000.
Hence, the correct answer is option 'C' (16000).
Rate of interest = 10%
Difference between compound interest and simple interest = $248.10
To find: The principal amount (Sum)
Let's assume the principal amount as P.
Calculation:
1. Simple Interest after 2 years:
Simple Interest = (P * R * T) / 100
Where,
P = Principal amount
R = Rate of interest
T = Time period (in years)
Simple Interest = (P * 10 * 2) / 100 = 0.2P
2. Compound Interest compounded every 6 months:
Since the interest is compounded every 6 months, the effective rate of interest for 2 years will be half of the given rate. So, the effective interest rate for compound interest will be 5%.
Compound Interest = P * (1 + R/100)^n - P
Where,
P = Principal amount
R = Rate of interest
n = Number of times interest is compounded per year (in this case, 2 years)
Compound Interest = P * (1 + 5/100)^4 - P = 1.2155P - P = 0.2155P
3. Difference between compound interest and simple interest:
Difference = Compound Interest - Simple Interest
248.10 = 0.2155P - 0.2P
248.10 = 0.0155P
To find P, divide both sides of the equation by 0.0155:
P = 248.10 / 0.0155 = 16000
Therefore, the principal amount (Sum) is $16,000.
Hence, the correct answer is option 'C' (16000).
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