A man saves Rs.1850 in January 2017 and increases his saving by 105 every month over the previous month. What is the annual saving for the man in the year 2017? (In Rs.)

Given:

Initial savings in January = ₹1850

Increment in monthly savings = ₹105

Number of months in a year = 12

Formula used:

Annual savings = Sum of monthly savings

Monthly savings form an arithmetic progression (AP):

Sum of n terms of an AP, S_n = n/2 × [2a + (n-1)d]

Where:

n = Number of months

a = First term (Initial savings in January)

d = Common difference (Increment in monthly savings)

Calculation:

Here, a = ₹1850, d = ₹105, n = 12

⇒ S₁₂ = 12/2 × [2 × 1850 + (12 - 1) × 105]

⇒ S₁₂ = 6 × [3700 + 11 × 105]

⇒ S₁₂ = 6 × [3700 + 1155]

⇒ S₁₂ = 6 × 4855

⇒ S₁₂ = ₹29130

∴ The correct answer is option (2).