Find the amount and the compound interest on Rs. 160000 for 2 years at 10% per annum, compounded half-yearly.

Present value, P = Rs.160000

Interest rate, R = 10% per annum

Time, n = 2 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 = 160000 [1 + (10/2)/100]⁴

⇒ A = 160000 [1 + 5/100]⁴

⇒ A = 160000 [1 + 1/20]⁴

⇒ A = 160000 [21/20]⁴

⇒ A = 160000 × 21/20 × 21/20 × 21/20 × 21/20

⇒ A = 160000 × 194481/160000

⇒ A = 1 × 194481

⇒ A = 194481

∴ Amount = Rs.8820

∴ Compound interest = Rs.(194481 – 160000) [∵CI = A – P]

= Rs.34481