Question

20. A sum becomes 33.1% more in three years when
invested under compound interest, interest being
compounded annually. Find the annual rate of interest.
(A) 10.5%
(B) 11.03%
(C) 10%
(D) 16.55%​

Answer 1

The annual rate of interest is 10%.

Correct option: (C) 10%

Step-by-step explanation:

Let the sum be P and rate of compound interest r% per year.

Then, final amount after 3 years

= $P(1+\dfrac{r}{100})^{3}$

Again, 33.1% more than P

= $P(1+\dfrac{33.1}{100})$

= $P\times 1.331$

According to the question,

$P(1+\dfrac{r}{100})^{3}=P\times 1.331$

⇒ $(1+\dfrac{r}{100})^{3}=1.331$

⇒ $1+\dfrac{r}{100}=\sqrt[3]{1.331}=1.1$

⇒ $\dfrac{r}{100}=0.1$

⇒ r = 10%

Thus the annual rate of interest is 10%.

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