Question

Swati borrowed Rs. 40960 from a bank to buy a piece of land. If the bank charges 12 (1/2)% per annum, compounded half-yearly, what amount will she have to pay after 1 (1/2)% years? Also, find the interest paid by her.

Answer 1

Present value, P = Rs.40960 

Interest rate, R = (25/2)% per annum 

Time, n = 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 = 40960 [1 + (25/4)/100]³ [R = 25/2 and n = 3/2 years] 

⇒ A = 40960 [1 + 1/16]³ 

⇒ A = 40960 [17/16]³ 

⇒ A = 40960 × 4913/4096 

⇒ A = 10 × 4913 

⇒ A = 49130 

∴ Amount = Rs.49130 

∴ Compound interest = Rs.(49130 – 40960) [∵CI = A – P] 

= Rs.8170