Question

Sanjay borrowed $ 12800 at the rate of 6*1/4 % per annum at simple interest. On the same day , he lent it to Rajesh at the same rate but compounded annually . What does sanjay gain at the end of 2 years?

Answer 1

In 1st case,
Simple Interest = Principle*Rate*Time/100 = 12800*25/4*2/100= 1600
Amount = Principle + SI = 12800+1600 = $14400
In 2nd case,
Amount = P(1+R/100)^n
= 12800(1+25/4/100)²
=12800*(1+25/400)²= 12800*425/400*425/400 = $14450
Gain = 14450-14400 = $50

Answer 2

• The amount that should be payed by Rajesh to Sanjay :

     Amount = P[1+r/100]ⁿ

                    = $ 12800 x [ 1+25/400] ²

                     = $12800 x 17/16 x 17/16

                      = $12800 x 289/256

                     = $14450

SI = [prt]/100

   = 12800 x 25/400 x 2

  = $1600

Sanjay had to pay amount = 12800+1600

                                                 = 14400

Gain = 14450 - 14400 =$50

Thank u.

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