## SOLVED CAIIB COMBINED PAPER 9:

**1. Example of "Annuity" is ...**

a. EMI of loan account

b. RD

c. Both of the above

d. None of the above

Ans - c

2. X wants to send his daughter to a management school after 5 years and will need onetime payment of charges amounting to Rs. 7 lac. At 12% roi, how much he should invest annually?

a. 111087

b. 110187

c. 118107

d. 118017

Ans - b

Explanation :

Here,

FV = 7 lac

R = 12% p.a.

T = 5 yrs

FV = P / R * [(1+R)^T - 1]

700000 = P * (1.125 – 1) ÷ 0.12

700000 = P * 6.352847

P = 110187

3. A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn at random , What is the probability that marble drawn is white ?

a. 2/5

b. 1/2

c. 3/8

d. 10/13

Ans – b

Solution :

Here Red = 3

Green = 7

White = 10

Hence total sample space is (3+7+10)= 20

Out of 20 one ball is drawn n(S) = { c ( 20,a.} = 20

Now here the probability of occurrence of White ball is said to hence out of 10 white ball n( R ) ={ c(10,a. }= 10

Hence P(R) = n(R)/n(S)

= 10/20 = 1/2

4. Ashwini purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 6 years. If YTM is increased by 1%, the change in price of bond would be......

a. 48.64

b. 44.86

c. 46.84

d. 46.88

Ans - b

Explanation :

If YTM is 9%, then bond’s price

= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6

= 955.14

So, change in price of the bond

= 1000 - 955.14

= Rs. 44.86 decrease

5. X opened a recurring account with a bank to deposit Rs. 16000 by the end of each year @ 10% roi. How much he would get at the end of 3rd year?

a. 52960

b. 52690

c. 52069

d. 52096

Ans - a

Explanation :

Here,

P = 16000

R = 10% p.a.

T = 3 yrs

FV = P / R * [(1+R)^T - 1]

FV = 16000 * (1.13 – 1) ÷ 0.1

= 52960

6. Which of the following is not a method of selecting samples from a population?

a. Judgement sampling

b. Random sampling

c. Probability sampling

d. Cluster Sampling

Ans - c

7. A card is drawn at random from a deck of cards. Find the probability of getting 3 of diamond.

a. 1/52

b. 1/38

c. 3/56

d. 3/38

Ans - a

Solution :

Since a pack consist 52 cards and among that cards there are 13 diamonds.

Now for same space { A card is drawn out of 52 cards i.e n( S ) = ( 52,a. = n( S ) = 52

Now for event for occurring 3 of diamonds in one drawn out of 13= n( E ) = 1 ( If you look at the 13 diamond cards the number 3 diamond card is just 1 )

Hence probability of occurrence of getting 3 of diamond

P(E)= n(E)/n(S)

= 1/52

8. Monica purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4 years. If YTM is increased by 1%, the change in price of bond would be......

a. 23.69

b. 32.69

c. 23.96

d. 32.39

Ans - d

Explanation :

If YTM is 9%, then bond’s price

= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4

= 967.604

So, change in price of the bond

= 1000 - 967.604

= 32.39 decrease

9. If there is a indirect relationship between rainfall & yield of crops, then...

a. yield is higher if rainfall is less

b. yield is lower if rainfall is less

c. yield is higher if rainfall is higher

d. none of the above

Ans - a

10. Suppose you start a rent-a-car business and want to buy an automobile. You have choice of buying the car cash down for Rs 400,000 or paying Rs. 90,000 a year for five years for the same car. What will be your choice, if the opportunity cost is 10% ?

a. Pay cash

b. Take the auto loan

c. Data insufficient to answer

d. None of these

Ans – b

Solution :

Here PV of Rs 90,000 each year for the next 5 years will be..

PV(90000,10%,5) = { 90000×(1.10^5-a. } / 0.10 ×1.1^5

= 341171

Now as the Cash down payment is 400,000 greater than the PV of Rs. 90,000 for next 5 years (Rs. 341171, you will prefer taking loan)

11. What is the price of a 20-year, zero-coupon bond with a 5.1% yield and Rs. 1000 face value?

a. Rs. 359

b. Rs. 369

c. Rs. 379

d. Rs. 389

Ans - b

Solution :

PV = 1000/(1+0.051)^20

= 369

12. An bag contains 10 black balls and 5 white balls. 2 balls are drawn from the bag one after other without replacement. What is the probability that both drawn are black ?

a. 2/7

b. 3/7

c. 4/7

d. 6/7

Ans - b

Solution :

Let E and F denote respective events that first and second ball drawn are black.

We have to find here P(E), P(E/F) and P(E n F )

Now P(E) = P(Black in first drawn) = 10/15

Also given that the first ball is drawn i.e events E has occurred. Now there are 9 black balls and 5 white balls left in the urn.

Therefore the probability that the second ball drawn is black, given that the ball first drawn is black nothing but conditional

probability of F given that E has occurred already.

Hence P(E/F) = 9/14

Now by the multiplication rule of probability

P(E n F) = P(E) × P(E/F)

= 10/15 × 9/14 = 3/7

a. EMI of loan account

b. RD

c. Both of the above

d. None of the above

Ans - c

2. X wants to send his daughter to a management school after 5 years and will need onetime payment of charges amounting to Rs. 7 lac. At 12% roi, how much he should invest annually?

a. 111087

b. 110187

c. 118107

d. 118017

Ans - b

Explanation :

Here,

FV = 7 lac

R = 12% p.a.

T = 5 yrs

FV = P / R * [(1+R)^T - 1]

700000 = P * (1.125 – 1) ÷ 0.12

700000 = P * 6.352847

P = 110187

3. A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn at random , What is the probability that marble drawn is white ?

a. 2/5

b. 1/2

c. 3/8

d. 10/13

Ans – b

Solution :

Here Red = 3

Green = 7

White = 10

Hence total sample space is (3+7+10)= 20

Out of 20 one ball is drawn n(S) = { c ( 20,a.} = 20

Now here the probability of occurrence of White ball is said to hence out of 10 white ball n( R ) ={ c(10,a. }= 10

Hence P(R) = n(R)/n(S)

= 10/20 = 1/2

4. Ashwini purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 6 years. If YTM is increased by 1%, the change in price of bond would be......

a. 48.64

b. 44.86

c. 46.84

d. 46.88

Ans - b

Explanation :

If YTM is 9%, then bond’s price

= [80 × (1.09^6 – 1) ÷ 0.09 + 1000] ÷ 1.09^6

= 955.14

So, change in price of the bond

= 1000 - 955.14

= Rs. 44.86 decrease

5. X opened a recurring account with a bank to deposit Rs. 16000 by the end of each year @ 10% roi. How much he would get at the end of 3rd year?

a. 52960

b. 52690

c. 52069

d. 52096

Ans - a

Explanation :

Here,

P = 16000

R = 10% p.a.

T = 3 yrs

FV = P / R * [(1+R)^T - 1]

FV = 16000 * (1.13 – 1) ÷ 0.1

= 52960

6. Which of the following is not a method of selecting samples from a population?

a. Judgement sampling

b. Random sampling

c. Probability sampling

d. Cluster Sampling

Ans - c

7. A card is drawn at random from a deck of cards. Find the probability of getting 3 of diamond.

a. 1/52

b. 1/38

c. 3/56

d. 3/38

Ans - a

Solution :

Since a pack consist 52 cards and among that cards there are 13 diamonds.

Now for same space { A card is drawn out of 52 cards i.e n( S ) = ( 52,a. = n( S ) = 52

Now for event for occurring 3 of diamonds in one drawn out of 13= n( E ) = 1 ( If you look at the 13 diamond cards the number 3 diamond card is just 1 )

Hence probability of occurrence of getting 3 of diamond

P(E)= n(E)/n(S)

= 1/52

8. Monica purchased a bond with face value of Rs. 1000 and Coupon of 8% and maturity of 4 years. If YTM is increased by 1%, the change in price of bond would be......

a. 23.69

b. 32.69

c. 23.96

d. 32.39

Ans - d

Explanation :

If YTM is 9%, then bond’s price

= [80 × (1.09^4 – 1) ÷ 0.09 + 1000] ÷ 1.09^4

= 967.604

So, change in price of the bond

= 1000 - 967.604

= 32.39 decrease

9. If there is a indirect relationship between rainfall & yield of crops, then...

a. yield is higher if rainfall is less

b. yield is lower if rainfall is less

c. yield is higher if rainfall is higher

d. none of the above

Ans - a

10. Suppose you start a rent-a-car business and want to buy an automobile. You have choice of buying the car cash down for Rs 400,000 or paying Rs. 90,000 a year for five years for the same car. What will be your choice, if the opportunity cost is 10% ?

a. Pay cash

b. Take the auto loan

c. Data insufficient to answer

d. None of these

Ans – b

Solution :

Here PV of Rs 90,000 each year for the next 5 years will be..

PV(90000,10%,5) = { 90000×(1.10^5-a. } / 0.10 ×1.1^5

= 341171

Now as the Cash down payment is 400,000 greater than the PV of Rs. 90,000 for next 5 years (Rs. 341171, you will prefer taking loan)

11. What is the price of a 20-year, zero-coupon bond with a 5.1% yield and Rs. 1000 face value?

a. Rs. 359

b. Rs. 369

c. Rs. 379

d. Rs. 389

Ans - b

Solution :

PV = 1000/(1+0.051)^20

= 369

12. An bag contains 10 black balls and 5 white balls. 2 balls are drawn from the bag one after other without replacement. What is the probability that both drawn are black ?

a. 2/7

b. 3/7

c. 4/7

d. 6/7

Ans - b

Solution :

Let E and F denote respective events that first and second ball drawn are black.

We have to find here P(E), P(E/F) and P(E n F )

Now P(E) = P(Black in first drawn) = 10/15

Also given that the first ball is drawn i.e events E has occurred. Now there are 9 black balls and 5 white balls left in the urn.

Therefore the probability that the second ball drawn is black, given that the ball first drawn is black nothing but conditional

probability of F given that E has occurred already.

Hence P(E/F) = 9/14

Now by the multiplication rule of probability

P(E n F) = P(E) × P(E/F)

= 10/15 × 9/14 = 3/7