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