Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is Rs. 125000 and the Parishad charges interest at 12% per annum compounded half-yearly, find the interest paid by Aslam after a year and a half.

Initial value, P = Rs.125000

Interest rate, R = 12% per annum

Time, n = (1 + 1/2) years = 3/2 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 = 125000 [1 + (12/2)/100]³ [n = 3/2 years]

⇒ A = 125000 [1 + 6/100]³

⇒ A = 125000 [1 + 3/50]³

⇒ A = 125000 [53/50]³

⇒ A = 125000 × 53/50 × 53/50 × 53/50

⇒ A = 125000 × 148877/125000

⇒ A = 1 × 148877

⇒ A = 148877

∴ Amount = Rs.148877

∴ Compound interest = Rs.(148877 – 125000) [∵CI = A – P]

= Rs.23877

∴ Rs.23877 interest paid by Aslam after (3/2) years.