Question : Sita deposited Rs. 5000 at 10% Simple interest for 2 years. How much more money will Sita have in her account at the end of two years, if it is compounded semi-annually?
Option 1: Rs. 50
Option 2: Rs. 40
Option 3: Rs. 77.50
Option 4: Rs. 85.50
Correct Answer: Rs. 77.50
Solution :
Given: $P$ = Rs. 5000, $R$ = 10%, and $T$ = 2 years
So, simple interest = $\frac{5000×10×2}{100}=1000$
If compounded semi-annually, $R$ =$\frac{10}{2}=5$%, $T$ = 4
Compound interest = $[P(1+\frac{R}{100})^{t}–1]$
= $[5000(1+\frac{5}{100})^{4}–1]$
= $[5000(\frac{194481}{160000})–1]$
= $\frac{5000×34481}{160000}$
= Rs. 1077.50
$\therefore$ Required difference = 1077.5 – 1000 = 77.50
Hence, the correct answer is Rs. 77.50.
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