Assertion (A) : Mr. Sharma deposited ₹ 80 per month in a cumulative deposit account for 6 years at the rate of 6% p.a. Qualifying sum of his whole deposit = ₹ 6811.20

Reason (R) : Let a sum ₹ P be deposited every month in a bank for n months. If the rate of interest be r% p.a., then interest on the whole deposit (I) = $P \times \dfrac{n(n + 1)}{12} \times \dfrac{r}{100}$.

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true.

4. Both A and R are false.

If sum ₹ P is deposited every month in a bank for n months and the rate of interest is r% p.a., then interest on the whole deposit (I) = $P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}$.

∴ Reason (R) is false.

Given,

Mr. Sharma deposited ₹ 80 per month in a cumulative deposit account for 6 years at the rate of 6% p.a.

By formula,

Qualifying sum = $P \times n + P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}$

P = ₹ 80/month

r = 6%

n = (6 × 12) = 72

Substituting values we get :

$\text{Qualifying sum} = 80 \times 72 + 80 \times \dfrac{72(72 + 1)}{2 \times 12} \times \dfrac{6}{100} \\[1em] = 5760 + 80 \times \dfrac{72 \times 73}{24} \times \dfrac{6}{100} \\[1em] = 5760 + \dfrac{20 \times 72 \times 73}{100} \\[1em] = 5760 + \dfrac{5256}{5} \\[1em] = 5760 + 1051.20 \\[1em] = \text{₹ 6811.20}$

∴ Assertion (A) is true.

Hence, Option 1 is the correct option.