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A person deposits some amount at a certain rate of compound interest. If he got
  • a)
    5%
  • b)
    10%
  • c)
    20%
  • d)
    4%
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A person deposits some amount at a certain rate of compound interest. ...
Let Principal (P) = 100
Amount (A) = 1.21*P = 1.21*100 = 121
Let rate of interest be x
A = P(1+x/100)2
121 = 100 [(100+x)/100]2
[(100+x)/100]2 = 121/100
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Most Upvoted Answer
A person deposits some amount at a certain rate of compound interest. ...
To solve this question, we need to calculate the compound interest for different interest rates. Compound interest is calculated on the principal amount, and the interest earned in each period is added to the principal for the next period's calculation.

Let's assume the principal amount deposited is P, and the time period is n years. The formula to calculate the compound interest is:

A = P(1 + r/n)^(n*t)

Where:
A = the final amount after n years
P = principal amount
r = interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years

We need to calculate the final amount for each interest rate option and compare the results.

1. 5% interest rate:
A = P(1 + 0.05/1)^(1*t)
A = P(1.05)^t

2. 10% interest rate (correct answer):
A = P(1 + 0.10/1)^(1*t)
A = P(1.10)^t

3. 20% interest rate:
A = P(1 + 0.20/1)^(1*t)
A = P(1.20)^t

4. 4% interest rate:
A = P(1 + 0.04/1)^(1*t)
A = P(1.04)^t

Comparing the formulas, we can see that the amount A is multiplied by the factor (1 + r/n)^(n*t). As the interest rate increases, the factor also increases, resulting in a higher final amount after the given time period.

Since we want to find the correct answer, we need to choose the option that gives the highest final amount. Based on the formulas above, the 10% interest rate option gives the highest factor (1.10^t) among all the given interest rates.

Hence, the correct answer is option 'B' - 10%.
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