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If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years is Rs. 48, then the principle amount must be
  • a)
    Rs. 550
  • b)
    Rs. 500
  • c)
    Rs. 375
  • d)
    Rs. 400
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the difference between the simple interest and compound interest on...
Solve using options. If we try 500 (option b) for convenience, we can see that the difference between the two is Rs. 64 (as the SI would amount to 300 and Cl would amount to 100 + 120 + 144 = 364). Since, we need a difference of only Rs. 48 we can realize that the value should be 3/4th of 500. Hence, 375 is correct.
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Most Upvoted Answer
If the difference between the simple interest and compound interest on...
To solve this problem, we can use the formula for compound interest and the formula for simple interest.

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for

The formula for simple interest is given by:

A = P(1 + rt)

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = the annual interest rate (in decimal form)
t = the number of years the money is invested or borrowed for

In this problem, we are given that the difference between the simple interest and compound interest is Rs. 48. We are also given that the interest rate is 20% per annum and the investment period is 3 years.

Let's assume the principal amount is P.

The compound interest can be calculated using the compound interest formula:

CI = P(1 + r/n)^(nt) - P

And the simple interest can be calculated using the simple interest formula:

SI = P(1 + rt) - P

Given that the difference between the simple interest and compound interest is Rs. 48, we can set up the equation:

SI - CI = 48

P(1 + rt) - P - [P(1 + r/n)^(nt) - P] = 48

Simplifying the equation:

Prt - P - Prt(1 + r/n)^(nt) + P = 48

Pr - Pr(1 + r/n)^(nt) = 48

Pr[1 - (1 + r/n)^(nt)] = 48

Pr[(1 + r/n)^(nt) - 1] = 48

Pr = 48 / [(1 + r/n)^(nt) - 1]

Now, substituting the given values, we have:

P = 48 / [(1 + 0.2/1)^(1*3) - 1]

P = 48 / [(1 + 0.2)^3 - 1]

P = 48 / [(1.2)^3 - 1]

P = 48 / [1.728 - 1]

P = 48 / 0.728

P = Rs. 65.93

Therefore, the principal amount must be Rs. 65.93.

Since none of the given options match Rs. 65.93, it seems there might be an error in the problem statement or the provided options.
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If the difference between the simple interest and compound interest on some principal amount at 20% per annum for 3 years is Rs. 48, then the principle amount must bea)Rs. 550b)Rs. 500c)Rs. 375d)Rs. 400Correct answer is option 'C'. Can you explain this answer?
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