Q. 124.4( 34 Votes )

# Abhay borrowed Rs. 16000 at 7% per annum simple interest. On the same day, he lent it to Gurmeet at the same rate but compounded annually. What does he gain at the end of 2 years?

Answer :

Present value = Rs.16000

Interest rate = 7% = (15/2) % per annum

Time = 2 years

Simple interest (SI) = PRT/100 [where, P = Present value

R = Interest rate, T = Time]

∴ SI = (16000 × (15/2) × 2)/100

⇒ SI = 160 × 15

⇒ SI = 2400

Now,

Amount (A) = P (1 + R/100)^{n} [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = 16000 [1 + (15/2)/100]^{2}

⇒ A = 16000 [1 + 3/40]^{2}

⇒ A = 16000 [43/40]^{2}

⇒ A = 16000 × 1849/1600

⇒ A = 10 × 1849

⇒ A = 18490

∴ Amount = Rs.18490

∴ Compound interest = Rs.(18490 – 16000)

= Rs.2490

Now,

(CI – SI) = 2490 -2400

= Rs.90

∴ Abhay gains Rs.90 at the end of 2 years.

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