__MODULE B : BUSINESS MATHEMATICS__

## 1. When coding for odd number of periods.

The following is done :

a. subtract each value from the smallest value

b. subtract each value from the highest value

c. subtract each value from the middlemost term

d. none of the above

Ans – c

2. A time series of annual data will contain which of the following components :

a. secular trend b. cyclical fluctuation

c. seasonal variation d. a & b

Ans – d

3. Suppose you purchased a bond Rs.1000 for Rs.920. The interest is 10 percent, and it will mature in 10 years.

Calculate Yield to maturity :

a. 10.75 % b. 11.00 % c. 11.25 % d. 11.50 %

Ans – c

Solution :

C=Coupon payment F=Face value

P=Price n=Years to maturity

Yield To Maturity = C + ( F - P / n ) / ( F + P / 2 )

=100+(1000-920/10)/(1000+920/2)

=100+(80/10)/(1920/2)

=100+8/960

=108/960

=0.1125

__=11.25%__

4. 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)

5. Find the present value of quarterly payment of Rs. 250 for 5 years @ 12% compounded quarterly.

a. 3179 b. 3019 c. 3109 d. 3719

Ans - d

Explanation :

Here, P = Rs. 250

T = 5 years = 5 × 4 = 20 quarters

R = 12% = 12% ÷ 4 = 0.03% quarterly

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

PV = 250 × (1.0320 – 1) ÷ (0.03 × 1.0320)

__= 3719__

5. What is the discount factor for Re. 1 to be received at the end of 2 yr with prevalent rate of 8% ?

a. 0.890 b. 0.873 c. 0.857 d. 0.842

Ans - c

Solution :

= 1/(1+r)n

= 1/(1.08)^2

__= 0.857__

6. There is a pattern of change within a year and the pattern is regular in ......

a. secular trend b. cyclical fluctuation

c. seasonal variation d. irregular variation

Ans - c

7. The value of the variable is unpredictable and changing in a random manner in ......

a. secular trend b. cyclical fluctuation

c. seasonal variation d. irregular variation

Ans - d

8. Pick the correct sentence(s):

a. Cyclical variation tends to oscillate above and below the secular trend line for periods longer than a year.

b. Seasonal variation makes a complete regular cycle within each year and does not affect one year any more than another.

c. both a and b

d. none of these

Ans – c

9. A bond has been issued with a face value of Rs. 1000 at 10% Coupon for 3 years. The required rate of return is 8%. What is the value of the bond if the Coupon amount is payable on half-yearly basis?

a. 1520 b. 1052 c. 1205 d. 1025

Ans - b

__Explanation :__

Here, FV = 1000

CR = 10% half-yearly = 5% p.a.

Coupon = FV × CR = 50 R = 8% yearly = 4% p.a. **14** t = 3 years

Bond Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value) __= 1052 (Since Coupon rate > YTM, so FV < Bond’s Value)__

10. An investment at 10% is compounded monthly, what shall be the effect interest rate for this?

a. 10.18 % b. 10.25 % c. 10.47 % d. 10.51 %

Ans - c

__Solution : __

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

__= 10.47__

11. A console bond of Rs. 10000 is issued at 6%. Coupon current interest rates and 9%. Find out the current value of the console bond.

a. Rs.7660 b. Rs.6760 c. Rs.6667 d. Rs.6676

Ans - c

__Solution : __

= 10000*0.06/0.09

= 6000/0.09

__= 6670__

12. A 15 year, 8 % Rs 1000 face value bond is currently trading at Rs 958. The YTM of this bond must be......

a. less than 8% b. equal to 8%

c. greater than 8% d. unknown

Ans – c

13. To convert an annual trend equation to a monthly basis, when original data are given as totals ......

a. 'a' is divided by 12 and 'b' by 144

b. 'a' is divided by 12 and 'b' by 12

c. 'a' is divided by 144 and 'b' by 12 **139**

d. 'a' is divided by 144 and 'b' by 144

Ans - a

14. Changes that have taken place as a result of such forces that could not be predicted floods etc. are known as ......

a. seasonal variations b. erratic variation

c. cyclical variation d. none of the above

Ans - b

15. Seasonal variations repeat during a period of ......

a: 12 months b. 24 months c. 36 months d. 46 months

Ans - a

16. Debentures are ......

(i) Normal types of bonds issued by Corporates,

(ii) It is unsecured debt, backed only by the name and goodwill of the Company,

(iii) In the event of the liquidation of the corporation, holders of debentures are repaid before stockholders, but after other secured creditors

a. Only (i) and (ii) b. Only (i) and (iii)

c. Only (ii) and (iii) d. (i), (ii) and (iii)

Ans - d

17. Based upon the concept of present value, a bond that paid a "below market" rate of interest (say 3%), would sell at ......

a. A price above its maturity value

b. A price equal to its maturity value

c. A price below as maturity value

d. None of the above.

Ans - c

18. The most important factors covering Magna' variations are ......

(i) growth of population, (ii) technological improvements, (iii) weather

a. Only (i) and (ii) b. Only (i) and (iii)

c. Only (ii) and (iii) d. (i), (ii) and (iii)

Ans - d

19. The general movement persisting over long period Is called ......

a. secular trend b. seasonal trend

c. trend value d. none of the above

Ans - a

20. The Value of a bond is ......

a. Its Face Value b. Present value of its future Cash flows c. Market Price d. Issue price

Ans - b

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