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A person earns an interest of 240 on investing certain amount at Simple interest for 2 years at 5 percent amount. If the rate of interest is compounded annually then how much more interest will be gain by the person at same rate of interest and on the same sum.
  • a)
    6
  • b)
    8
  • c)
    12
  • d)
    10
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A person earns an interest of 240 on investing certain amount at Simpl...
240 = P*(5/100)*2, P = 2400
CI = 2400(1+5/100)2 – 2400 = 246
So, 246 – 240 = 6
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Most Upvoted Answer
A person earns an interest of 240 on investing certain amount at Simpl...
Given:
Principal amount = p
Time = 2 years
Rate of interest = 5%
Simple interest earned = 240

Calculating the principal amount:
Simple interest = (p * r * t)/100
240 = (p * 5 * 2)/100
p = 240 * 100 / 10 = 2400

So, the principal amount is 2400.

Calculating the compound interest:
Compound interest formula = p(1+r/n)^(nt) - p
Where p is the principal amount, r is the rate of interest, n is the number of times interest is compounded in a year, and t is the time period.

As the rate of interest is compounded annually,
n = 1
r = 5%
t = 2 years

Compound interest = p(1+r/n)^(nt) - p
= 2400(1+0.05/1)^(1*2) - 2400
= 2400(1.05)^2 - 2400
= 2520 - 2400
= 120

So, the compound interest earned is 120.

Calculating the difference in interest:
Difference in interest = Compound interest - Simple interest
= 120 - 240
= -120

The difference in interest is negative, which means there is no gain in interest by the person. In fact, the person would earn 120 less in compound interest compared to simple interest. Therefore, the correct answer is option A) 6.
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Community Answer
A person earns an interest of 240 on investing certain amount at Simpl...
240 = P*(5/100)*2, P = 2400
CI = 2400(1+5/100)2 – 2400 = 246
So, 246 – 240 = 6
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