At what rate percent per annum will 4000 amount to 4410 in 2 years 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.

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At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years?

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Solution

Principal (P) = Rs. 4000 C.I = Rs. 410 ∴ Amount (A) = Rs. 4000 + 410 = Rs. 4410 Let rate =R% p.a. Period (n) = 2 years. ∴ Amount =P(1+R100)n ⇒AP=(1+R100)2 ⇒Rs.44104000=(1+R100)n ⇒4414000=[1+R100]2 ⇒(2120)2=(1+R100)2 Comparing, we get 1+R100=2120=1+120 ∴R100=120⇒R=10020=5 ∴ Rate =5% p.a

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