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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