Question

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Answer 1

Question :

John borrowed a sum of Rs. 15625 from Donald at the rate of 16 % per annum under simple interest. Immediately John gave this money to Bush at the same rate under compound interest, compounded quarterly. Find the profit of John in doing so after 9 months.

Answer :

John borrowed a sum of Rs. 15625 from Donald at the rate of 16 % per annum under simple interest.

Sum of money borrowed by John from Donald i.e Principal ( P ) = Rs. 15625

Rate of interest per annum ( R ) = 16 %

Time ( T ) = 9 months = 9 / 12 years = 0.75 years

Simple interest = PTR / 100

= 15625 × 0.75 × 16 / 100

= 187500 / 100

= 1875

i.e Simple that has to paid by John = Rs. 1875

John gave this money to Bush at the same rate under compound interest, compounded quarterly.

Principal ( P ) = Rs. 15625

Rate of interest per quarter ( R ) = ( 1 / 4 ) × 16 = 4 %

Compound interest when compounded quarterly = P × { ( 1 + R / 100 )^( 4T ) - 1 }

= 15625 × { ( 1 + 4 / 100 )^( 4 × 0.75 ) - 1 }

= 15625 ×{ ( 104/100 )³ - 1 }

= 15625 × ( 1.04³ - 1 )

= 15625 × ( 1.124864 - 1 )

= 15625 × 0.124864

= 1951

i.e CI that Bush will pay to John = Rs. 1951

Profit gained by john by doing so = CI - SI = Rs. 1951 - Rs. 1875 = Rs. 76

Hence, the profit of John in doing so after 9 months is Rs. 76.