The compound interest on Rs. 40000 at 6% per annum for 6 months, compo

1.	The compound interest on Rs. 40000 at 6% per annum for 6 months, compounded quarterly, is A. Rs. 1209 B. Rs. 1902 C. Rs. 1200 D. Rs. 1306
Answer» 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

The compound interest on Rs. 40000 at 6% per annum for 6 months, compounded quarterly, is A. Rs. 1209 B. Rs. 1902 C. Rs. 1200 D. Rs. 1306

Answer»

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 [203/200]²

⇒ 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