Question : In 3 years, Rs. 3000 amounts to Rs. 3993 at $x$% compound interest compounded annually. The value of $x$ is ___.
Option 1: $10$
Option 2: $8$
Option 3: $5$
Option 4: $3\frac{1}{3}$
Correct Answer: $10$
Solution :
Principal = Rs. 3000, Amount = Rs. 3993, Time = 3 years and Rate of interest = $x$%
Now, applying the formula of compound interest,
Amount = $p(1+\frac{r}{100})^t$
⇒ $3000(1+\frac{x}{100})^3=3993$
⇒ $(1+\frac{x}{100})^3=\frac{3993}{3000}$
⇒ $(1+\frac{x}{100})^3=\frac{1331}{1000}$
⇒ $(1+\frac{x}{100})^3=(\frac{11}{10})^3$
⇒ $1+\frac{x}{100}=\frac{11}{10}$
⇒ $\frac{x}{100}=\frac{11}{10}–1$
⇒ $x=\frac{1}{10}×100$
⇒ $x=10$
Hence, the correct answer is $10$.
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