Question : A sum of INR 10,000 was invested at a rate of 10% per annum for 2 years, compounded half-yearly. Find the compound interest.
Option 1: 2,151.0625
Option 2: 2,055
Option 3: 2,255
Option 4: 2,155.0625
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Correct Answer: 2,155.0625
Solution :
Given, Principal, $P=\mathrm{INR\ }10000,$ Rate, $r=10\%=0.10,$
As it compounded half-yearly, the time will be 2 × 2 = 4 years
$\text{Total Amount, A}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
⇒ $A=10000(1+\frac{\frac{10}{100}}{2})^{4}$
⇒ $A=10000(\frac{21}{20})^4$
⇒ $A=10000×\frac{441}{400}×\frac{441}{400}$
$\therefore A=12155.0625$
Now, Compound interest = Total amount – Principal = 12155.0625 – 10000 = INR 2,155.0625
Hence, the correct answer is 2,155.0625.
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