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
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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