36. A owes B $ 1350 due in 3 months and B owes A $ 1078 due 5 months. If they agrees to settle their account right now at 5 % p.a, A should pay to B :

1. 1. $ 277	1
      	3

   
   
   

   2. $ 288.25

   
   
   

   3. $ 302

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question , we have
   

   P.W. of $ 1350 =	1350 x 100	=	1350 x 400	= $ 1,333.33
   	100 + [ ( 3 / 12 ) x 5 ]		405

   
   

   Correct Option: A

   According to question , we have
   

   P.W. of $ 1350 =	1350 x 100	=	1350 x 400	= $ 1,333.33
   	100 + [ ( 3 / 12 ) x 5 ]		405

   
   

   P.W. of $ 1078 =	1078 x 100	=	1078 x 1200	= $ 1056
   	100 + [ ( 5 / 12 ) x 5 ]		1225

   
   

   ∴ A should pay B = $		4000	- 1056
   		3

   
   

   A should pay B = $	832	= $ 277	1
   	3		3

   
   

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37. A bill is discounted at 5 % per annum. If banker’s discount be allowed, at what rate of interest must the proceeds be invested, so that nothing is lost?

1. 1. 5%

   
   
   

   2. 4	19	%
      	20

      
      

   
   
   

   3. 5	5	%
      	9

      
      

   
   
   

   4. 10%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the sum be $ 100.
   Then, B.D. = $ 5 Proceeds = $ (100 - 5) = $ 95
   ∴ $ 5 must be the interest on $ 95 for 1 year.

   Correct Option: C

   Let the sum be $ 100.
   Then, B.D. = $ 5 Proceeds = $ (100 - 5) = $ 95
   ∴ $ 5 must be the interest on $ 95 for 1 year.
   

   So, rate =		100 x 5		= 5	5	%
   		95 x 1			19

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38. The discount on $ 5229 due in 1 year 9 months reckoning compound interest at 5 % is :
    

1. 1. $ 429.00

   
   
   

   2. $ 415.00

   
   
   

   3. $ 393.25

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   P.W =	5229
   	[(1 + 5 / 100)][1 + (3 / 4)(5 / 100)]

   
   

   Correct Option: A

   P.W =	5229
   	[(1 + 5 / 100)][1 + (3 / 4)(5 / 100)]

   
   

   = 5229 x	20	x	80	= $ 4800
   	21		83

   
   ∴ T.D. = $ (5229 - 4800) = $ 429.
   

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39. Find the present worth (P.W.) and the true discount reckoning 6 % per annum simple interest of $ 176 due in 20 months time.
    

1. 1. $ 160, $ 16

   
   
   

   2. $ 130, $ 46

   
   
   

   3. $ 150, $ 26

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , simple interest = $ 176 , Rate = 6% , Time = 20 months = ( 20/12 ) years
   

   ∴ Present worth =	Simple interest x Rate x Time
   	100 + Rate x Time

   
   

   Present worth =	100 x 76
   	100 + [ 2 x ( 20/12 ) ]

   Correct Option: A

   Here , simple interest = $ 176 , Rate = 6% , Time = 20 months = ( 20/12 ) years
   

   Present worth =	100 x 76
   	100 + [ 2 x ( 20/12 ) ]

   
   

   Present worth =	100 x 76	= $ 160
   	100 + 10

   
   True discount = Amount - Present worth
   True discount = $ 176 - $ 160 = $ 16.
   

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40. A bill which being due at the end of 4 years is now worth $ 575, but if it is due in 2 years 6 months, it would now be worth $ 620. The sum of the bill is :
    

1. 1. $ 695

   
   
   

   2. $ 725

   
   
   

   3. $ 713

   
   
   

   4. None of these
      

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let, the rate p.c. be r%.
   Given :- Present worth = $ 575 and Time = 4 years
   Let, $ x be the amount of the bill.
   

   ∴ Present worth =	Amount x Rate x Time
   	100 + Rate x Time

   
   

   Then, 575 =	x × 100
   	100 + 4r

   
   That is, 57500 + 2300r = 100x
   ∴ x = 575 + 23r …(1)
   Present worth = $ 620 and Time = 2 years and 6 months = 2.5 years
   

   and 620 =	100x
   	100 + 2.5 r

   Correct Option: C

   Let, the rate p.c. be r%.
   Given :- Present worth = $ 575 and Time = 4 years
   Let, $ x be the amount of the bill.
   

   ∴ Present worth =	Amount x Rate x Time
   	100 + Rate x Time

   
   

   Then, 575 =	x × 100
   	100 + 4r

   
   That is, 57500 + 2300r = 100x
   ∴ x = 575 + 23r …(1)
   Present worth = $ 620 and Time = 2 years and 6 months = 2.5 years
   

   and 620 =	100x
   	100 + 2.5 r

   
   ∴ 62000 + 1550r = 100x
   ∴ 6200 + 155r = 10x = 5750 + 230r [using (1)]
   ∴ 75r = 450
   ∴ r = 6
   Putting the value of x in eq. (1) ⇒ x = 575 + 138 = $ 713.
   Hence , The sum of the bill is $ 713.

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