Find the amount and the compound interest on Rs. 12800 for 1 year at 7% per annum, compounded half-yearly.

Present value, P = Rs.12800

Interest rate, R = (15/2)% 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 = 12800 [1 + (15/4)/100]²

⇒ A = 12800 [1 + 3/80]²

⇒ A = 12800 [83/80]²

⇒ A = 12800 × 6889/6400

⇒ A = 128 × 6889/64

⇒ A = 2 × 6889

⇒ A = 13778

∴ Amount = Rs.13778

∴ Compound interest = Rs.(13778 – 12800) [∵CI = A – P]

= Rs.978