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