At what rate per cent per annum will 5000 amount to Rs. 5832 in 2 year

1.	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» 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 %.

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»

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 %.