A certain sum of money (₹ P) is lent for $3\dfrac{1}{2}$ years at r% C.I. compounded half yearly. The interest accrued will be:

1. $P\Big(1 + \dfrac{r}{100}\Big)^{\dfrac{7}{2}} - P$

2. $P\Big(1 + \dfrac{r}{100}\Big)^3 \times \Big(1 + \dfrac{r}{2 \times 100}\Big)^1 - P$

3. $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{\dfrac{7}{2}} - P$

4. $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^7 - P$

A certain sum of money (₹ P) is lent for $3\dfrac{1}{2}$ years at r% C.I. compounded yearly. The interest accrued will be:

1. $P \Big(1 + \dfrac{r}{100}\Big)^{\dfrac{7}{2}} - P$

2. $P\Big(1 + \dfrac{r}{100}\Big)^3 \times \Big(1 + \dfrac{r}{2 \times 100}\Big)^1 - P$

3. $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{\dfrac{7}{2}} - P$

4. $P\Big(1 + \dfrac{r}{2 \times 100}\Big)^7 - P$

Statement 1: The population of a town in the year 2024 is x and it increases by 10% every year. The population of in the year 2021 was = x $\Big(1 - \dfrac{10}{100}\Big)^3$

Statement 2: If the population increases from year 2021 to year 2024 at the rate of 10%, then corresponding decrease from 2024 to 2021 is 10 x 3%.

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Assertion (A): A certain sum of money P let out at r% C.I. increased for first 5 years and then decreased for next five years at the same rate is same as decrease on the same sum at the same rate (r%) during the first five years and then increase further next five years at the same rate.

Reason (R):

$P\Big(1 + \dfrac{r}{100}\Big)^5 \times P\Big(1 - \dfrac{r}{100}\Big)^5$ is same as $P\Big(1 - \dfrac{r}{100}\Big)^5 \times P\Big(1 + \dfrac{r}{100}\Big)^5$.

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are true, and R is the correct reason for A.

4. Both A and R are true, and R is the incorrect reason for A.