Assertion (A) : Sunidhi deposits ₹1,600 per month in a bank for $1\dfrac{1}{2}$ years in a recurring deposit account at 10% p.a. She gets ₹31,080 on maturity.

Reason (R): Maturity value is given by MV = (P x n) - S.I.

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.

A is true, R is false

Reason

According to Assertion:

Given,

P = ₹1,600

n = $1\dfrac{1}{2}$ years = 18 months

r = 10%

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

$\therefore I = 1600\times \dfrac{18\times 19}{2 \times 12} \times \dfrac{10}{100} \\[1em] I = 1600 \times \dfrac{342}{24} \times 0.1 \\[1em] I = 1600 \times 14.25 \times 0.1 \\[1em] I = ₹2,280$

Sum deposited = ₹1,600 x 18 = ₹28,800

Maturity value = Sum deposited + Interest = ₹28,800 + ₹2,280 = ₹31,080

So, Assertion(A) is true.

According to Reason:

Maturity value is given by MV = (P x n) - S.I.

But ,

Maturity value = Sum deposited + Interest

Sum deposited = P × n

Maturity value = (P × n) + Interest

So, Reason is false.

Hence, Option 1 is the correct option.