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?
- A.
Between Rs. 2P and 2.5P
- B.
Between Rs. 2.5P and 3P
- C.
Between 3P and 3.5P
- D.
Between 3.5P and 4P
Attempted by 5 students.
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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.
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).
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
Conclusion:
The calculated amount is approximately 3.97P. This value falls between 3.5P and 4P.