Find the rate of interest for a sum of money

Find the rate of interest for a sum of money which becomes 1.728 times itself in 3 years, if the interest is compounded annually.
उस धनराशि के लिए ब्याज दर ज्ञात कीजिए जो 3 वर्षों में स्वयं की 1.728 गुनी हो जाती है, यदि ब्याज की गणना वार्षिक चक्रवृद्धि रुप से होती है।

20% 22% 15% 25%

Detailed Solution & Logic

Correct Answer:

20%

$ \text\frac{A}{P} $ = 1.728, n = 3 years compounded annually
Compound Interest formula: A = P $ (1 + \frac{r}{100})^n $
$ (1 + \frac{r}{100})^3 = 1.728 $
$ 1 + \frac{r}{100} = \sqrt[3]{1.728} $
$ 1 + \frac{r}{100} = \frac{6}{5} $
$ \frac{r}{100} = \frac{6}{5} - 1 = \frac{1}{5} $
$ r = \frac{1}{5} \times 100 = 20% $
Answer: 20%

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