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A owes B Rs 1573 payable \(1\frac12\) years hence. Also B owes A Rs 1444.50 payable 6 months hence. If they want to settle the account forth with, keeping 14 % as the rate of interest, then who should pay whom and how much ? 

(a) A to B, Rs 28.50 

(b) B to A, Rs 37.50 

(c) A to B, Rs 50 

(d) B to A, Rs 50

1 Answer

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Best answer

(d) B to A, Rs 50

Let the present value of what A owes B be Rs x. 

Then, x + \(\frac{x\times14\times3}{2\times100} = 1573\)

⇒ x + \(\frac{21x}{100}\) 1573 ⇒ \(\frac{21x}{100}\) = 1573

⇒ x = \(\frac{1573\times100}{121}=1300\)

Let y be the present value of what B owes A. 

Then, y + y x \(\frac12\times\frac{14}{100}\) = 1444.50

⇒ y + \(\frac{7y}{100}\) = 1444.50 ⇒ 107 y = 1444.50 x 100

⇒ y = \(\frac{144450}{107}\) = Rs 1350

Hence B must pay Rs 50 to A.

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