Find the amount and the compound interest on Rs. 8000 for 1 year at 10% per annum, compounded half-yearly.

Present value, P = Rs.8000

Interest rate, R = 10% per annum

Time, n = 1 years

∵ Compounded half-yearly.

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

R = Annual interest rate

n = Time in years]

∴ A = 8000 [1 + (10/2)/100]²

⇒ A = 8000 [1 + 5/100]²

⇒ A = 8000 [1 + 1/20]²

⇒ A = 8000 [21/20]²

⇒ A = 8000 × 441/400

⇒ A = 20 × 441

⇒ A = 8820

∴ Amount = Rs.8820

∴ Compound interest = Rs.(8820 – 8000) [∵CI = A – P]

= Rs.820