CBSE Questions for Class 11 Commerce Applied Mathematics Basics Of Financial Mathematics Quiz 16 - MCQExams.com

$${\textbf{Step  - 1: Framing the formula for finding the rate of decrease}}{\text{.}}$$

                    $${\text{Let the rate of increase in the population be }}r,$$

                    $${\text{We know, population increases geometrical progression so, we}}$$

                    $${\text{will use the compound interest formula}}{\text{.}}$$

                    $${\text{Given}},{\text{ }}P{\text{ }} = {\text{ }}16,000$$

                    $${\text{Time period }},{\text{ }}n{\text{ }} = {\text{ }}2$$

                    $${\text{Population after }}2{\text{ yrs }},{\text{ }}A{\text{ }} = {\text{ }}17640$$

                    $${\text{Using the formula of compound interest, we can write}}$$

                    $$A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$$

                    $$17640 = 16000{\left( {1 + \dfrac{r}{{100}}} \right)^2}$$

$${\textbf{Step  - 2: Solving the above equation to find the rate of decrease}}{\text{.}}$$

                    $$\dfrac{{17640}}{{16000}} = {\left( {1 + \dfrac{r}{{100}}} \right)^2}$$

                    $$\dfrac{{441}}{{400}} = {\left( {1 + \dfrac{r}{{100}}} \right)^2}$$

                    $${\text{Taking square root on both the sides,}}$$

                    $$\dfrac{{21}}{{20}} = 1 + \dfrac{r}{{100}}$$

                    $$\dfrac{1}{{20}} = \dfrac{r}{{100}}$$

                    $$r = 5%$$

$${\textbf{Hence, the rate of decrease of population is 5% }}{\text{.}}$$