The compound interest on Rs. 4000 at 10% per annum for 2 years 3 month

1.	The compound interest on Rs. 4000 at 10% per annum for 2 years 3 months, compounded annually, is A. Rs. 916 B. Rs. 900 C. Rs. 961 D. Rs. 896
Answer» Present value, P = Rs.4000 Interest rate, R = 10% per annum Time, n = 2 years 3 months = (2 + 1/4) years ∴ Amount (A) = P (1 + R/100)ⁿ × [1 + (R/4)/100] [Where, P = Present value R = Annual interest rate n = Time in years] ∴ A = 4000 (1 + 10/100)² × [1 + (10/4)/100] ⇒ A = 4000 (1 + 1/10)² × [1 + 1/40] ⇒ A = 4000 (11/10)² × [41/40] ⇒ A = 4000 × 121/100 × 41/40 ⇒ A = 40 × 121 × 41/40 ⇒ A = 121 × 41 ⇒ A = 4961 ∴ Amount = Rs.4961 ∴ Compound interest = Rs.(4961 – 4000) [∵CI = A – P] = Rs.961

The compound interest on Rs. 4000 at 10% per annum for 2 years 3 months, compounded annually, is A. Rs. 916 B. Rs. 900 C. Rs. 961 D. Rs. 896

Answer»

Present value, P = Rs.4000

Interest rate, R = 10% per annum

Time, n = 2 years 3 months = (2 + 1/4) years

∴ Amount (A) = P (1 + R/100)ⁿ × [1 + (R/4)/100] [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = 4000 (1 + 10/100)² × [1 + (10/4)/100]

⇒ A = 4000 (1 + 1/10)² × [1 + 1/40]

⇒ A = 4000 (11/10)² × [41/40]

⇒ A = 4000 × 121/100 × 41/40

⇒ A = 40 × 121 × 41/40

⇒ A = 121 × 41

⇒ A = 4961

∴ Amount = Rs.4961

∴ Compound interest = Rs.(4961 – 4000) [∵CI = A – P]

= Rs.961