Calculate the compound interest on ₹72,000 at the rate of 9% per annum for 18 months when interest is compounded half yearly (rounded off up to the nearest ₹).

Given:

Principal (P) = ₹72,000

Rate (r) = 9% per annum

Time (t) = 18 months = 1.5 years

Interest is compounded half yearly

Formula used:

A = P(1 + r/n)^nt

Where,

n = number of times interest applied per time period (half yearly, so n = 2)

A = Amount

Calculations:

A = 72000(1 + 9/(2×100))^2×1.5

⇒ A = 72000(1 + 0.045)³

⇒ A = 72000(1.045)³

⇒ A = 72000 × 1.1411

⇒ A = 82163.96

Compound Interest (CI) = A - P

⇒ CI = 82163.96 - 72000

⇒ CI = ₹10,163.96

Rounded to nearest ₹, CI = ₹10,164

∴ The correct answer is option 1.