Question : A sum becomes Rs. 33800 in 2 years and Rs. 43,940 in 3 years, when lent in a scheme of compound interest (compounding annually). If double the sum is invested in the same scheme for 2 years, then what will be the amount obtained at the end of 2 years?
Option 1: Rs. 62480
Option 2: Rs. 67600
Option 3: Rs. 71240
Option 4: Rs. 60420
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Correct Answer: Rs. 67600
Solution : When compounded annually, $ A= P(1+\frac{R}{100})^{T}$, Where A is the total amount, P is the principal amount, R is the rate of interest per annum, and T is the time in years." $ 33800= P(1+\frac{R}{100})^{2}$.....................(I) $ 43940= P(1+\frac{R}{100})^{3}$.................(II) Dividing equation II by I, we get, $\frac{43940}{33800}=1+\frac{R}{100}$ $⇒\frac{R}{100} =\frac{43940}{33800}-1$ $⇒\frac{R}{100} =\frac{10140}{33800}$ $⇒ R = 30\%$ Put R = 30% in equation I, we get, $33800= P(1+\frac{30}{100})^{2}$ $⇒33800= P×\frac{13}{10}×\frac{13}{10}$ $⇒P = 20000$ Now, when the Principal is double, which means 2 × 20000 = 40000, Total amount $= 40000 (1+\frac{30}{100})^{2}=40000×\frac{13}{10}×\frac{13}{10}=67600$ Hence, the correct answer is Rs. 67600.
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