At what rate per cent per annum will Z 640 amount to Rs. 774.40 in 2 years when compounded annually?
Let rate = R % per annum
P = Rs.640
A = Rs.774.40
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
⇒ 774.40 = 640 (1 + R/100)2
⇒ (1 + R/100)2 = 774.40/640
⇒ (1 + R/100)2 = 1.21
⇒ (1 + R/100) = √(1.21)
⇒ R/100 = (1.1) - 1
⇒ R/100 = 0.1
⇒ R = 0.1 × 100
⇒ R = 10
∴ Rate = 10% per annuam.