Question : A sum amounts to Rs. 6,120 in 2 years and Rs. 7,340 in 3 years at Compound Interest. The sum (in Rs.) is (rounded off to 2 decimal places):
Option 1: 4,050.13
Option 2: 4,254.63
Option 3: 4,850.32
Option 4: 4,560.23
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Correct Answer: 4,254.63
Solution : Given: A sum amounts to Rs. 6,120 in 2 years and Rs. 7,340 in 3 years at Compound Interest. We know the formula, $A = P \left(1 + \frac{r}{100}\right)^t$ Where $A$ is the final amount after $t$ years, $P$ is the principal amount and $r$ is the annual interest rate. Interest on Rs. 6,120 for 1 year = Rs. 7,340 – Rs. 6,120 = Rs. 1,220 The rate of interest = $\frac{1,220}{6,120}$ × 100 = 19.93464 Let the sum be Rs. $x$ So, $x \left(1 + \frac{19.93464}{100}\right)^2 = 6120$ ⇒ $x=4254.63$ Hence, the correct answer is 4254.63.
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