A person deposit ₹P, every month for n months at R percent per annum, simple interest in a recurring deposit account.

Assertion (A): The maturity value is more than total amount deposited by the person.

Reason (R): Maturity value includes an interest equal to $\dfrac{\text{P} \times \text{n(n + 1)} \times \text{R}}{2400}$

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Given,

Amount deposited per month = ₹ P

Time = n months

Rate of interest = R%

The total amount deposited is the monthly deposit multiplied by the number of months.

Total deposited = P x n

The interest earned is given by the formula = $\text{P} \times\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{R}}{100}$

The maturity value is the total deposited amount plus the interest earned.

Maturity value = P x n + $\text{P} \times\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{R}}{100}$

The maturity value includes the total deposited amount plus the interest earned, which is a positive value.

∴ The maturity value is more than total amount deposited by the person.

So, assertion (A) is true.

By formula,

Interest = $\text{P} \times\dfrac{\text{n(n + 1)}}{2 \times 12} \times \dfrac{\text{R}}{100}$

= $\dfrac{\text{P} \times \text{n(n + 1)} \times \text{R}}{2400}$

So, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.