A owes B Rs 1573 payable \(1\frac12\) years hence. Also B owes A Rs 14

1.	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
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.

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

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.