Swati borrowed Rs. 40960 from a bank to buy a piece of land. If the ba

1.	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» 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

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»

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