At what rate per cent per annum will Rs. 4000 amount to Rs. 4410 in 2 years when compounded annually?

Let rate = R % per annum

P = Rs.4000

A = Rs.4410

Time = 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]

∴ A = P (1 + R/100)²

⇒ 4410 = 4000 (1 + R/100)²

⇒ (1 + R/100)² = 4410/4000

⇒ (1 + R/100)² = 441/400

⇒ (1 + R/100) = √(441/400)

⇒ R/100 = (21/20) - 1

⇒ R/100 = (21 – 20)/20

⇒ R/100 = 1/20

⇒ R = 100/20

⇒ R = 5

∴ Rate = 5% per annuam.