Ram deposits Rs. P with a bank at r% compound interest and sees it reach…

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Ram deposits Rs. P with a bank at r% compound interest and sees it reach Rs.16P in 20 years. If he had invested the same amount at r% simple interest for 20 years, what would be the amount?

  1. A.

    Between Rs. 2P and 2.5P

  2. B.

    Between Rs. 2.5P and 3P

  3. C.

    Between 3P and 3.5P

  4. D.

    Between 3.5P and 4P

Attempted by 5 students.

Show answer & explanation

Correct answer: D

Step-by-Step Solution

To determine the amount under Simple Interest, we first need to estimate the interest rate (r) from the Compound Interest scenario.

  1. Analyze Compound Interest:

    • Given: P * (1 + r)^20 = 16P

    • Simplify: (1 + r)^20 = 16

    • Since 16 is 2^4, we can write: (1 + r)^20 = 2^4

    • Taking the 20th root of both sides: 1 + r = 2^(4/20) = 2^(1/5)

    • 2^(1/5) is approximately 1.1487 (or about a 14.87% annual interest rate).

  2. Analyze Simple Interest:

    • Simple Interest formula for Amount (A): A = P * (1 + r * t)

    • A = P * (1 + 0.1487 * 20)

    • A = P * (1 + 2.974)

    • A = 3.974P

  3. Conclusion:

    • The calculated amount is approximately 3.97P. This value falls between 3.5P and 4P.

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