Question

At what rate per cent per annum will 5000 amount to Rs. 5832 in 2 years, compounded annually? 

A. 11% 

B. 10% 

C. 9% 

D. 8%

Answer 1

Present value, P = Rs.5000 

Amount, A = Rs.5832 

Time, n = 2 years 

Now, 

Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest 

P = Present value 

R = Annual interest rate 

n = Time in years] 

∴ Amount (A) = P (1 + R/100)ⁿ 

⇒ 5832 = 5000 (1 + R/100)² 

⇒ (1 + R/100)² = 5832/5000 

⇒ (1 + R/100)² = 2916/2500 

⇒ (1 + R/100)² = (54/50)2 

⇒ 1 + R/100 = 54/50 

⇒ R/100 = (54/50) - 1 

⇒ R/100 = (54 – 50)/50 

⇒ R/100 = 4/50 

⇒ R = 400/50 

⇒ R = 8 

∴ Rate = 8 %.