The compound interest on Rs. 40000 at 6% per annum for 6 months, compounded quarterly, is
Present value, P = Rs.40000
Interest rate, R = 6% per annum
Time, n =6 months = 1/2 years
∵ Compounded quarterly.
∴ Amount (A) = P [1 + (R/4)/100]4n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 40000 [1 +(6/4) /100]2 [4n = 4 × 1/2]
⇒ A = 40000 [1 + 3/200]2
⇒ A = 40000 [1 + 3/200]2
⇒ A = 40000 [203/200]2
⇒ A = 40000 × 203/200 × 203/200
⇒ A = 40000 × 203/200 × 203/200
⇒ A = 200 × 203 × 203/200
⇒ A = 1 × 203 × 203
⇒ A = 41209
∴ Amount = Rs.41209
∴ Compound interest = Rs.(41209 – 40000) [∵CI = A – P]
= Rs.1209