Find the amount and the compound interest on Rs. 6000 for 1 year at 10% per annum compounded half-yearly.

Present value = Rs.6000

Interest rate = 10 % per annum

Time = 1 years

∵ Interest is compounded half-yearly.

∴ Amount (A) = P [1 + (R/2)/100]²ⁿ [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = 6000 [1 + (10/2)/100]²

⇒ A = 6000 [1 + 5/100]²

⇒ A = 6000 [1 + 1/20]²

⇒ A = 6000 [21/20]²

⇒ A = 6000 × 21/20 × 21/20

⇒ A = 300 × 21 × 21/20

⇒ A = 15 × 21 × 21

⇒ A = 6615

∴ Amount = Rs.6615

∴ Compound interest = Rs.(6615 – 6000)

= Rs.615