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41. A sum of Rs 2550 is borrowed to be paid back in two years by equal annual payments, 4 per cent, compound interest being allowed . What is the annual payment?
  A.  Rs 1352
  B.  Rs 1345
  C.  Rs 1320
  D.  Rs 1300
     
   
View Answer

Shortcut:
To find equal annual payments: A sum of Rs A is borrowed to be paid back in 'n' years in 'n' equal annual payments, R per cent compound interest being allowed. Then the value of annual payment is given by Rs
A / (100/R)[1 - {100/(100+R)}n]

Here, A = 2550, n = 2, R = 4
Using these values in the shortcut, we get:
Required payment =
2550 / (100/4)[1 − {100/(100 + 4)}2]

=
2550 / 25 x [1 − (100/104)2]

=
2550 / 25 x [1 − (25/26)2]

=
2550 / 25 x [1 − (25 x 25/26 x 26]

=
2550 / 25 x [1 − 625/676]

=
2550 / 25 x (676 − 625)/676

=
2550 / (25 x 51)/676

=
2550 x 676 / 25 x 51
= 2 x 676 = 1352
Hence, the annual payment is Rs 1352.

42. If Rs 10 be allowed as true discount no a bill of Rs 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
  A.  20.11
  B.  18.33
  C.  17.55
  D.  19.25
     
   
View Answer

SI on Rs (110 -10) for a given time = Rs 10
SI on Rs 100 for double the time = Rs 20
Sum = Rs (100 + 20) = Rs 120
TD on Rs 110 = Rs (
20 / 120
x 110 = Rs 18.33
Hence, the discount allowed is Rs 18.33.

43. Rs 20 is the true discount on Rs 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same:
  A.  10.80
  B.  10.10
  C.  10.40
  D.  11.50
     
   
View Answer

SI on Rs 240 for a given time = Rs 20
SI on Rs 240 for half the time = Rs 10
∴ Rs 10 is TD on Rs 250
So, TD on Rs 260 = Rs(
10 / 250
x 260 = Rs 10.40
Hence, the discount allowed is Rs 10.40.

44. A has to pay Rs 220 to B after 1 year. B asks A to pay Rs110 in cash and defer the payment of Rs110 for 2 years. A agrees to it. Counting, the rate of interest at 10% per.
  A.  A gains Rs. 5.44
  B.  A gains Rs. 7.54
  C.  A gains Rs. 7.34
  D.  A gains Rs. 6.42
     
   
View Answer

A has to pay the PW of Rs 220due 1 year hence, which is Rs(
100 x 220 / 100 + (10 x 1)
= Rs 200
A actually pays = Rs [110 + PW of Rs 110 due 2 years hence] = Rs(110 +
100 x 110 / 100 + (8 x 2)
= Rs 192.66
∴ A gains = Rs [200 - 192.66] = Rs 7.34

45. A owes B Rs 456.75 payable 4
1 / 2
months hence and B owes A Rs 455.51 payable 3 months hence. If they agree to settle their account by a ready money payment, what sum should be paid over and to whom, reckoning the rate of true discount at 4 per cent per annum?
  A.  Re1,A
  B.  Re3,B
  C.  Re1,B
  D.  Re2,A
     
   
View Answer

time = 4
1 / 2
months =
3 / 8
year, rate = 4%
∴ amount of Rs 100 = Rs(
203 / 2

∴ PW = Rs 456.75 ÷
203 / 2
x 100 = Rs 450
Again, time = 3 months =
1 / 4
year, rate = 4%
PW = Rs 455.51 x
100 / 104
= Rs 451
Hence the required sum to be paid to A = Rs 451 − Rs 450 = Re 1

46. Find the true discount reckoning 3 per cent per annum simple interest of Rs 1802 due in 2 years time.
  A.  Rs 100
  B.  Rs 105
  C.  Rs 98
  D.  Rs 102
     
   
View Answer

Shortcut:
To find true discount when rate, amount/sum and time are given. True Discount (TD) =
A x R x T / 100 + RT

where A = Amount, R = rate and T = time
Here, A = 1802, R = 3, T = 2
Using these values in the shortcut, we get:
True Discount (TD) =
1802 x 3 x 2 / 100 + (3 x 2)

=
1802 x 6 / 106
= 17 x 6 = 102
Hence, the true discount is Rs 102.

47. If the difference between the interest and discount on a certain sum of money for 6 months at 6% be Rs 2.25.Fnd the sum.
  A.  Rs 2575
  B.  Rs 2505
  C.  Rs 2485
  D.  Rs 2620
     
   
View Answer

Shortcut:
To find the difference between simple interest (SI) and True Discount (TD), when amount (A), rate (R) and time (T) are given. SI − TD =
A x (RT)2 / 100(100 + RT)
]
Here, A = ?, R = 6, T = 6/12 or 1/2, SI − TD = 2.25
Using these values in the shortcut, we get:
SI − TD =
A x (6 x 1/2)2 / 100(100 + 6 x 1/2)
]
2.25 =
A x 3 x 3 / 100(100 + 3)
]
2.25 =
A x 3 x 3 / 100 x 103

2.25 x 100 x 103 = 9A
A =
225 x 103 / 9
= 2575
Hence, the sum is Rs 2575.

48. The true discount on Rs 340 due 5 years hence is Rs40.Find the rate per cent.
  A.  2
2 / 3
%
  B.  3
3 / 2
%
  C.  3
4 / 3
%
  D.  5
2 / 3
%
     
   
View Answer

Shortcut:
To find the rate when True Discount (TD), amount (A) and time (T) are given. R =
100 x TD / (A − TD) x T

Here, A = 340, R = ?, TD = 40, T = 5
Using these values in the shortcut, we get:
R =
100 x 40 / (340 − 40) x 5

=
4000 / 300 x 5
=
8 / 3
= 2
2 / 3

Hence, the rate is 2
2 / 3
%.

49. Find the present value of Rs 1051.25 due a year hence at 5
1 / 8
%.
  A.  Rs 1100
  B.  Rs 1000
  C.  Rs 1150
  D.  Rs 1020
     
   
View Answer

Shortcut:
To find Present Worth when rate, amount and time are given. Present Worth (PW) =
100 x A / 100 + RT

where A = Amount, R = rate and T = time
Here, A = 1051.25, R = 5
1 / 8
=
41 / 8
, T = 1
Using these values in the shortcut, we get:
Present Worth (PW) =
100 x 1051.25 / 100 + (41/8 x 1)

=
105125 / 100 + 41/8

=
105125 x 8 / 800 + 41

=
105125 x 8 / 841
= 125 x 8 = 1000
Hence, the present value is Rs 1000.

50. Find the true discount on Rs 226.59 due in one year 9 months, reckoning compound interest at 5%.
  A.  Rs 18.20
  B.  Rs 17.50
  C.  Rs 19.40
  D.  Rs 18.59
     
   
View Answer

Shortcut:
To find the present worth of A rupees due 'n' years hence at 'r' per cent compounded interest payable annually, (i) A = Present Worth x (1 +
r / 100
)n
(ii) Present Worth =
A / (1 + r/100)n
)
(iii) True Discount = Amount − Present Worth
Here, A = 226.59, n = 1
3 / 4
, R = 5
Using these values in the shortcut, we get:
Present Worth =
226.59 / [1 + (5/ 100)]7/4
)
=
226.59 / [1 + (1/ 20)] x [1 + (3/80)]

=
226.59 / [(20 + 1)/20] x [(80 + 3)/80]

=
226.59 / 21/20 x 83/80

=
226.59 x 20 x 80 / 21 x 83
= 208
True Discount = A − PW = 226.59 − 208 = Rs 18.59
Hence, the true discount is Rs 18.59.

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