Question : At a certain sum of money with the interest rate of 6% per annum for 4 years, the simple interest is Rs. 4500. Find the compound interest (compounding annually) of 2 years at the same sum when the rate of interest is 4% per annum.
Option 1: Rs. 1,530
Option 2: Rs. 1,430
Option 3: Rs. 1,830
Option 4: Rs. 1,560
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Correct Answer: Rs. 1,530
Solution : Simple Interest $= \frac{P\times R\times T}{100}$ ⇒ $4500 = \frac{P × 6 × 4}{100}$ ⇒ $P = \frac{4500 × 100}{6 × 4}$ ⇒ $P = 750 × 25 = \text{Rs. }18750$ Now, Compound Interest $= P(1 + \frac{R}{100})^T- P$ ⇒ $CI= 18750(1 + \frac{4}{100})^2 - 18750$ ⇒ $CI = 18750\times(\frac{26}{25})^2 - 18750$ ⇒ $CI = 18750 × \frac{676}{625} - 18750$ ⇒ $CI = 20280 - 18750 =1530$ Hence, the correct answer is Rs. 1530.
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