If the amount is 2(1/4) times of the sum after 2 years, then the rate of compound interest must be (a) 60% (b) 40% (c) 64% (d) 50%

Question

If the amount is \(2\frac{1}{4}\) times of the sum after 2 years, then the rate of compound interest must be 

(a) 60% 

(b) 40% 

(c) 64% 

(d) 50%

Answer 1

(d) 50%

Let the sum be Rs x. Then, Amount =Rs \(\frac{9X}{4}\)

n = 2, r = ?

\(\therefore\) \(\frac{9X}{4}\) = x\(\big(1+\frac{r}{100}\big)^2\)

\(\Rightarrow\) \(\frac{9}{4}\) = \(\big(1+\frac{r}{100}\big)^2\) \(\Rightarrow\) \(\big(\frac{3}{2}\big)^2\) = \(\big(1+\frac{r}{100}\big)^2\)

\(\Rightarrow\) \(\frac{r}{100}\) = \(\frac{3}{2}\) - 1 = \(\frac{1}{2}\) \(\Rightarrow\) r = 50% p.a.