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1. Find the present worth of Rs 461.25 due 2
1 / 2
years hence, rekoning simple interest at 4 p.c. per annum.
  A.  Rs 429.31
  B.  Rs 419.32
  C.  Rs 409.30
  D.  Rs 417.20
     
   
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 = 461.25, R = 4, T = 2
2 / 2
=
5 / 2

Using these values in the shortcut, we get:
Present Worth (PW) =
100 x 461.25 / 100 + (4 x 5/2)

=
46125 / 100 + 10

=
46125 / 110
= 419.32

2. Find the present worth(PW) and the true discount rekoning 6% per annum simple interest of Rs 176 due in 20 months time.
  A.  Rs 170,Rs 15
  B.  Rs 165,Rs 15
  C.  Rs 160,Rs 16
  D.  Rs 150,Rs 12
     
   
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 = 176, R = 6, T =
20 / 12

Using these values in the shortcut, we get:
Present Worth (PW) =
100 x 176 / 100 + (6 x 20/12)

=
100 x 176 / 100 + 10

=
100 x 176 / 110
= 160
Hence, the Present Worth is Rs 160.
Now, True discount = Amount − Present Worth
= 176 − 160 = 16
Hence, the true discount is Rs 16

3. I want to sell my bike.There are two offers, one at cash payment of Rs 8100 and another at a credit of Rs 8250 to be paid after 6 months. If money being worth 6 ¼% per annum simple interest, which is the better offer?
  A.  Rs 8150 in cash
  B.  Rs 8200 in cash
  C.  Rs 7950 in cash
  D.  Rs 8100 in cash
     
   
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 = 8250, R = 6
1 / 4
=
25 / 4
, T =
1 / 2

Using these values in the shortcut, we get:
Present Worth (PW) =
100 x 8250 / 100 + (25/4 x 1/2)

=
100 x 8250 / 100 + 25/8

=
100 x 8250 / (800 + 25)/8

=
100 x 8250 x 8 / 825
= 100 x 10 x 8 = 8000
∴ the Present Worth is Rs 8000.
Hence, Rs 8100 in cash is a better offer.

4. The present worth of Rs 1404 due in two equal half yearly instalments at 8% per annum simple interest is :
  A.  . Rs 1325
  B.  . Rs 1310
  C.  . Rs 1290
  D.  . Rs 1315
     
   
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 =
1404 / 2
= 702, R = 8, T =
1 / 2

Using these values in the shortcut, we get:
Present Worth due 6 months hence =
100 x 702 / 100 + (8 x 1/2)

=
100 x 702 / 100 + 4

=
100 x 702 / 104
= 675
∴ the Present Worth is Rs 675.
PW of Rs 702 due 1 year hence =
100 x 702 / 100 + (8 x 1)

=
100 x 702 / 108
= 650
∴ Total PW = Rs (675 + 650) = Rs 1325

5. A trader owes a merchant Rs 901 due 1 year’s hence.However, the trader want to settle the account after 3 months. How much cash should he pay,if the rate of interest is 8% per annum.
  A.  Rs840
  B.  Rs860
  C.  Rs850
  D.  Rs820
     
   
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 = 901, R = 8, T =
9 / 12

Using these values in the shortcut, we get:
Present Worth due 6 months hence =
100 x 901 / 100 + (8 x 9/12)

=
100 x 901 / 100 + 6

=
100 x 901 / 106
= 850
Hence, PW is Rs 850.

6. A man buys a watch for Rs 195 in cash and sells if for Rs220 at a credit of 1 year.If the rate of interest is 10% , the man:
  A.  Man loss Rs4.
  B.  Man gains Rs5.
  C.  Man gains Rs3.
  D.  Man loss Rs5.
     
   
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 = 220, R = 10, T = 1
Using these values in the shortcut, we get:
Present Worth due 1 year hence =
100 x 220 / 100 + 10

=
100 x 220 / 110
= 100 x 2 = 200
Hence, the man gains Rs 5.

7. A man purchased a cow for Rs. 300 and sold it the same day for Rs 360, allowing the buyer a credit of 9 years. If the rate of interest be 7
1 / 2
per annum., then the man has a gain of : 5%
  A.   2%
  B.   3%
  C.   6%
  D.   5%
     
   
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 = 360, R = 7
1 / 7
=
50 / 7
, T = 2
Using these values in the shortcut, we get:
Present Worth due 2 year hence =
100 x 360 / 100 + (50/7 x 2)

=
100 x 360 / 100 + 100/7

=
100 x 360 / (700 + 100)/7

=
100 x 360 x 7 / 800
= 45 x 7 = 315
Hence, the S.P is Rs 315.
∴ Gain % =
100 x 15 / 300
= 5 %

8. A owes B,Rs 1120 payable 2 years hence and B owes A, Rs 1081.50 payable 6 months hence.If they decide to settle their accounts forthwith by payment of ready money and the rate of interest by 6% per annum, then who should pay and how much:
  A.  B, Rs 45
  B.  B, Rs 60
  C.  B, Rs 50
  D.  B, Rs 30
     
   
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 = 1120, R = 6, T = 2
Using these values in the shortcut, we get:
Present Worth due 2 year hence =
100 x 1120 / 100 + (6 x 2)

=
100 x 1120 / 100 + 12

=
100 x 1120 / 112
= 1000
PW of Rs 1081.50 due 6 months hence at 6% =
100 x 1081.5 / 100 + (6 x 1/2)

=
100 x 1081.5 / 103
= 1050
So, A owes B, Rs 1000 cash and B owes A Rs 1050 cash.
∴ B must pay Rs 50 to A.

9. What is the present worth of Rs 272.61 due in 2 years 73 days at 7
1 / 2
per cent ?
  A.   Rs 234
  B.   Rs 230
  C.   Rs 236
  D.   Rs 228
     
   
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 = 272.61, R = 7
1 / 2
=
15 / 2
, T =
803 / 365

Using these values in the shortcut, we get:
Present Worth due 2 year and 73 days hence =
100 x 272.61 / 100 + (15/2 x 803/365)

=
100 x 272.61 / 100 + 2409/146)

=
100 x 272.61 / (14600 + 2409)/146)

=
27261 x 146 / 17009
= 234
Hence, the present value is Rs 234.

10. What sum will discharge a debt of Rs 5300 due a year and a half hence at 4 % per annum?
  A.  Rs. 4500
  B.  Rs. 5000
  C.  Rs. 5200
  D.  Rs. 5100
     
   
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 = 5300, R = 4, T = 1
1 / 2
=
3 / 2

Using these values in the shortcut, we get:
Present Worth due 1 and half year hence =
100 x 5300 / 100 + (4 x 3/2)

=
100 x 5300 / 100 + 6

=
100 x 5300 / 106

=
100 x 5300 / 106
= 5000
Hence, the present value is Rs 5000.

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