Question : The compound interest accrued on a sum of INR 20,000 at the end of 2 years compounded annually is INR 2,050. Find the compound interest at the end of the 3rd year.
Option 1: INR 3,153.50
Option 2: INR 2852.50
Option 3: INR 3,152.50
Option 4: INR 3,154.50
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Correct Answer: INR 3,152.50
Solution :
Principal = INR 20000
Time = 2 years
$\text{Compound interest}= \text{Total amount – Principal}$
$⇒\text{Compound interest}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}-\text{Principal}$
$⇒2050=20000((1+\frac{\text{Rate}}{100})^2-20000$
$⇒22050=20000((1+\frac{\text{Rate}}{100})^2$
$⇒(1+\frac{\text{Rate}}{100})^2=\frac{22050}{20000}=\frac{441}{400}$
$⇒(1+\frac{\text{Rate}}{100})^2=(\frac{21}{20})^2$
$⇒1+\frac{\text{Rate}}{100}=\frac{21}{20}$
$\therefore \text{Rate}=5$%
Now, the total amount after 3 years with a 5% compound interest on a sum of INR 20000
$=20000(1+\frac{5}{100})^3$
$=20000(\frac{21}{20})^3$
$=20000×\frac{441}{400}×\frac{21}{20}$
$=23152.50$
So, compound interest after 3 years = 23152.50 – 20000 = INR 3152.50
Hence, the correct answer is INR 3,152.50.
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