## SOLVED CAIIB COMBINED PAPER 7:

**1. A bond has been issued with a face value of Rs. 1000 at 8% Coupon for 3 years. The required rate of return is 7%. What is the value of the bond?**

a. 1062.25

b. 1625.25

c. 1026.25

d. 1052.25

Ans - c

Explanation :

Here,

FV = 1000

Coupon Rate (CR) = 0.08

t = 3 yr

R (YTM) = 0.07

Coupon = FV × CR = 80

Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)

So, Value of bond = 1026.25

(Since Coupon rate > YTM, so Bond’s Value > FV)

2. Seasonal variation is...

a. Repetitive

b. Predictable

c. Both a and b

d. None of the above

Ans - c

3. 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

Hence probability of occurrence of getting 3 of diamond

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

= 1/52

4. Suppose you deposit 2000/- each year for the next three years into an account that pays 8%. How much will you have in 3 years?

a. 6492.80

b. 6758.60

c. 6521.50

d. 6120.50

Ans – a

Solution :

FV of annuity = A/r ×{(1+r)^n-1}

Now FV = 2000/0.08×{(1+0.08)^3-1}

i.e Rs 6492.80

5. What is the two year discounting factor at a discount rate of 10% per year ?

a. 0.826

b. 1.212

c. 1.124

d. 0.456

Ans – a

Solution :

The formula to solve the said sum is 1/(1+r)^t where r = discount rate and t = period

Here r = 10 and t = 2

Discounting factor= 1/(1+0.10)^2

= 1/ 1.21

= 0.826

6. Amrita obtained a loan of Rs. 92820 @ 10%, which he has to pay in 4 equal annual installments. Calculate the amount of installment?

a. 22892

b. 22982

c. 28292

d. 29282

Ans - d

Explanation :

Here,

P = 92820

R = 10% p.a.

T = 4 yrs

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

EMI = 92820 × 0.1 × 1.14 ÷ (1.14– 1)

= 29282

7. A constant flow paid or received at regular time intervals for ever is known as...

a. Annuity

b. Perpetuity

c. Growing annuity

d. Growing perpetuity

Ans - b

8. An investment at 10% interest rate compounded monthly is equal to an effective annual rate of ...

A. 10.38 %

B. 10.47 %

C. 10.57 %

D. 10.68 %

Ans - b

Solution :

Effective Interest Rate = (1+r/n)^n - 1

= (1+0.10/12)^12 - 1

= (1.1047 - 1)*100

= 10.47 %

9. A bond has been issued with a face value of Rs. 20000 at 12% Coupon for 3 years. The required rate of return is 10%. What is the value of the bond?

a. 20595

b. 29095

c. 25095

d. 20995

Ans - d

Explanation :

Here,

FV = 20000

Coupon Rate (CR) = 0.12

t = 3 yr

R (YTM) = 0.10

Coupon = FV × CR = 2400

Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)

So, Value of bond = 20995

(Since Coupon rate > YTM, so FV < Bond’s Value)

10. We have six students say A, B, C, D, E, F participating in a quiz contest. Out of six students only two can reach to the final. What is the probability of reaching to the final of each student ?

a. 1/2

b. 2/3

c. 1/3

d. 1/6

Ans – c

Solution :

Since out of 6 , 2 can reach the final. Hence sample space is

n(S) = 6 c2 = 6!/(6-b.!×2! = 15

Here event of occurrence of probability of each student out of six ( A B C D E F ) = ( AB AC AD AE AF ) =n ( E ) = 5

Now P(E) = 5/15 = 1/3

11. The compound interest on a sum for 2 years is Rs. 153 and simple interest is 225 for 3 years. What are the ROI & the principal amount?

a. 5 & 1875

b. 4 & 1875

c. 5 & 1785

d. 4 & 1785

Ans - b

Explanation :

Let, principal amount = P,

ROI = R,

simple interest = SI,

compound interest = CI

SI for 3 years = 225, so SI for 2 years = 150

CI for 2 years = 153, so difference of Rs. 3 = interest for Rs. 75 (225-150)

So, R = 3/75 *100 = 4%

P = (SI × 100) ÷ (R×T)

= (225×100) ÷ (4×3)

= 1875

12. The probability that we associate with an interval estimate is called ...

a. Estimate level

b. Confidence Level

c. Probability Level

d. None of the above

Ans - b

a. 1062.25

b. 1625.25

c. 1026.25

d. 1052.25

Ans - c

Explanation :

Here,

FV = 1000

Coupon Rate (CR) = 0.08

t = 3 yr

R (YTM) = 0.07

Coupon = FV × CR = 80

Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)

So, Value of bond = 1026.25

(Since Coupon rate > YTM, so Bond’s Value > FV)

2. Seasonal variation is...

a. Repetitive

b. Predictable

c. Both a and b

d. None of the above

Ans - c

3. 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

Hence probability of occurrence of getting 3 of diamond

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

= 1/52

4. Suppose you deposit 2000/- each year for the next three years into an account that pays 8%. How much will you have in 3 years?

a. 6492.80

b. 6758.60

c. 6521.50

d. 6120.50

Ans – a

Solution :

FV of annuity = A/r ×{(1+r)^n-1}

Now FV = 2000/0.08×{(1+0.08)^3-1}

i.e Rs 6492.80

5. What is the two year discounting factor at a discount rate of 10% per year ?

a. 0.826

b. 1.212

c. 1.124

d. 0.456

Ans – a

Solution :

The formula to solve the said sum is 1/(1+r)^t where r = discount rate and t = period

Here r = 10 and t = 2

Discounting factor= 1/(1+0.10)^2

= 1/ 1.21

= 0.826

6. Amrita obtained a loan of Rs. 92820 @ 10%, which he has to pay in 4 equal annual installments. Calculate the amount of installment?

a. 22892

b. 22982

c. 28292

d. 29282

Ans - d

Explanation :

Here,

P = 92820

R = 10% p.a.

T = 4 yrs

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

EMI = 92820 × 0.1 × 1.14 ÷ (1.14– 1)

= 29282

7. A constant flow paid or received at regular time intervals for ever is known as...

a. Annuity

b. Perpetuity

c. Growing annuity

d. Growing perpetuity

Ans - b

8. An investment at 10% interest rate compounded monthly is equal to an effective annual rate of ...

A. 10.38 %

B. 10.47 %

C. 10.57 %

D. 10.68 %

Ans - b

Solution :

Effective Interest Rate = (1+r/n)^n - 1

= (1+0.10/12)^12 - 1

= (1.1047 - 1)*100

= 10.47 %

9. A bond has been issued with a face value of Rs. 20000 at 12% Coupon for 3 years. The required rate of return is 10%. What is the value of the bond?

a. 20595

b. 29095

c. 25095

d. 20995

Ans - d

Explanation :

Here,

FV = 20000

Coupon Rate (CR) = 0.12

t = 3 yr

R (YTM) = 0.10

Coupon = FV × CR = 2400

Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)

So, Value of bond = 20995

(Since Coupon rate > YTM, so FV < Bond’s Value)

10. We have six students say A, B, C, D, E, F participating in a quiz contest. Out of six students only two can reach to the final. What is the probability of reaching to the final of each student ?

a. 1/2

b. 2/3

c. 1/3

d. 1/6

Ans – c

Solution :

Since out of 6 , 2 can reach the final. Hence sample space is

n(S) = 6 c2 = 6!/(6-b.!×2! = 15

Here event of occurrence of probability of each student out of six ( A B C D E F ) = ( AB AC AD AE AF ) =n ( E ) = 5

Now P(E) = 5/15 = 1/3

11. The compound interest on a sum for 2 years is Rs. 153 and simple interest is 225 for 3 years. What are the ROI & the principal amount?

a. 5 & 1875

b. 4 & 1875

c. 5 & 1785

d. 4 & 1785

Ans - b

Explanation :

Let, principal amount = P,

ROI = R,

simple interest = SI,

compound interest = CI

SI for 3 years = 225, so SI for 2 years = 150

CI for 2 years = 153, so difference of Rs. 3 = interest for Rs. 75 (225-150)

So, R = 3/75 *100 = 4%

P = (SI × 100) ÷ (R×T)

= (225×100) ÷ (4×3)

= 1875

12. The probability that we associate with an interval estimate is called ...

a. Estimate level

b. Confidence Level

c. Probability Level

d. None of the above

Ans - b