Find the rate percent per annum if rs 2000 amount to rs 2662 in 1½ ye

1.	Find the rate percent per annum if rs 2000 amount to rs 2662 in 1½ years interest being compounded half yearly
Answer» Step-by-step EXPLANATION: Given:- Principal = Rs.2000 Amount = Rs.2662 TIME = 1 ½ years Interest compounded HALF-yearly. To Find:- The RATE of interest. Solution:- Time = 1 ½ years = 3 half years The formula for finding Amount is:- $\leadsto \sf Amount = P \bigg(1 + \dfrac{r}{100}\bigg)^n$ Here:- • A = Amount = Rs.2662 • P = Principal = Rs.2000 • r = rate = ? • n = time = 3 half years Substituting the values:- $\implies \sf2662= 2000 \times \bigg(1 + \dfrac{r}{100}\bigg)^3$ $\implies \sf \dfrac{2662}{2000} = \bigg(1 + \dfrac{r}{100}\bigg)^3$ $\implies \sf 1.331 = \bigg(1 + \dfrac{r}{100}\bigg)^3$ $\implies \sf {(1.1)}^{3} = \bigg(1 + \dfrac{r}{100}\bigg)^3$ $\implies \sf 1.1= 1 + \dfrac{r}{100}$ $\implies \sf \dfrac{r}{100} = 1.1 - 1$ $\implies \sf \dfrac{r}{100} = 0.1$ $\implies \sf r = 0.1 \times 100$ $\implies \sf r = 10$ For half- yearly, Rate = 10% Rate% per annum = 20% $\large \underline{ \boxed{\sf \therefore \: \textsf{ \textbf{Rate \: of \: Interest = 20\%}}}}$