__MODULE B : BUSINESS MATHEMATICS__

## 1. The period of moving average is to be decided on the basis of ......

a. length of the cycle b. policies of the company

c. both the above d. none of the above

Ans - a

2. Treasury securities are ......

(i) Debt obligations of the Government, issued by the treasury department,

(ii) They are backed by the full faith and credit of the government,

(iii) They are considered to be free of default risk

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

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

Ans - d

3. Method of least squares is ......

a. flexible in nature b. non-flexible in nature

c. semi-flexible in nature d. none of the above

Ans - a

4. Which of the following is true about the Yield rate of bonds?

(i) It varies inversely with changes in the bond's market price,

(ii) It is the bond rate at bond maturity,

(iii) It is computed in the same manner as Dividend yield on stocks

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

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

Ans - a

5. In shifting the trend origin, the value of 'b' ......

a. changes b. remains unchanged

c. badly fluctuates d. None of the above

Ans - b

6. The moving average may constitute a satisfactory trend for a series that is of ......

(i) linear duration,

(ii) whose cycles are regular in duration

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

c. Either (i) or (ii) d. Both (i) and (ii)

Ans - d

7. Find the interest rate. Present Value is Rupees 100. Future Value becomes 115.76 in 3 years.

a. 4.5 % b. 5 % c. 5.5 % d. 6 %

Ans - b

__Solution :__

FV=115.76

PV=100

N=3

FV= PV(1+r)^n

115.76=100x(1+R)^3 (1+R)^3

=1.1576

r=0.0499

=0.05

__=5%__

8. If I take a loan of Rupees 8,000 and repay Rupees 225 per month, for 4 years, what is the effective annual rate on the loan?

a. 15.3 % b. 15.8 % c. 16.3 % d. 16.8 %

Ans - d

__Solution__

EMI=225

t=4 years*12=48 month

=225*48 = 10800-8000

= 2800 which is interest paid for 4 yrs

i.e. 48 month.

Hence 2800/8000*48

=0.35*48

**=**16.8%

9. Which method which helps draw a line between the set of scattered points

a. regression method b. correlation method

c. least square method d. least fit method

Ans - c

10. What is a zero coupon bond?

a. there is gain only in price b. gain in coupon

c. no gain at all d. none of these

Ans - a

11. What does the Central tendency theorem state ?

a. as the sample size increases the sampling distribution of the mean will approach normality irrespective of the shape of the population distribution

b. the mean of the sampling distribution of the mean will equal the population mean even if the population is not normal

c. uses of sample statistics to make inferences of the the population parameters without knowledge of the of the frequency distribution

d. all of the above

Ans - d

12. If the estimating equation is Y = a – b X. which of the following is true

a. the y intercept is b b. slope of line is negative

c. there is inverse relationship d. b & c

Ans - d

13. Mr. Amit purchased a property for Rs.8 lac. He has been assured to get Rs 10 lac, after one year at 9% interest rate.

What is the net present value of the property based on this assured return?

a. Rs. 117400 b. Rs. 118300 c. Rs. 119200 d. Rs. 120100

Ans - a

__Solution :__

1000000/1.09=917431-80000

__= 117400__

14. Current yield on an 8% Rs. 100 bond is 7.5%. The price of the bond is ......

a. 104.67 b. 105.67 c. 106.67 d. 107.67

Ans - c

__Explanation :__

Bond Price

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

(Here, t = 1 So, price

= (Coupon + Face Value) ÷ (1 + R)

= (8 + 100) ÷ 1.075 = 100.465)

But, since Coupon Interest

= Current Yield × Current Market Price

So, Price = 8 ÷ 7.5% = 8000 ÷ 75

__= 106.67__

15. You will be receiving Rs. 204000 at the end of each year for the next 20 years. If the current discount rate for such a stream of cash flow is 10%, find the present value of cash flow.

a. 1737760 b. 1736660 c. 1736770 d. 1737660

Ans - c

__Explanation :__

Here, P = 204000 R = 10 T = 20 PV

= P / R * [(1+R)^T - 1]/(1+R)^T __PV = 1736770__

16. The central limit theorem ......

a. Requires some knowledge of the frequency distribution b. Permits us to use sample statistics to make inferences about population parameters

c. Relates the shape of a sampling distribution of the mean to the man of the sample

d. Requires a sample to contain fewer than 30 observations

Ans - b

17. Find Coefficient of Variance for the values given :

{13,35,56,35,77}

a. 0.4156 b. 0.5164 ** ** c. 0.5614 d. 0.6514

Ans - c

__Explanation :__

Number of terms (N) = 5

Mean: Xbar = (13+35+56+35+77)/5 = 216/5 = 43.2

__Standard Deviation (SD):__

Formula to find SD is

σx= √(1/(N - 1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))

=√(1/(5-1)((13-43.2)2+(35-43.2)2+(56-43.2)2+(35-43.2)2+(77-43.2)2))

=√(1/4((-30.2)2+(-8.2)2+(12.9)2+(-8.2)2+(33.8)2))

=√(1/4((912.04)+(67.24)+(163.84)+(67.24)+(1142.44)))

=√(588.2)

=24.2528

__Coefficient of variation (CV)__

= Standard Deviation / Mean = 24.2528/43.2

= 0.5614

__Hence the required Coefficient of Variation is 0.5614__

18. Which one of the following is a component of time series ?

(i) secular trend, (ii) seasonal variations,

(iii) cyclical variations

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

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

Ans - d

19. We find irregular variations due to ......

(i) lock outs, (ii) transport bottlenecks (iii) floods

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

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

Ans - d

20. How can we remove seasonal variations ?

(i) reducing prices in seasons,

(ii) introducing different products having different seasons

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

c. Either (i) or (ii) d. Neither (i) nor (ii)

Ans - d

21. Coupon rate means ......

a. Market rate of return of a bond / Debenturre

b. The rate at which the bond would pay interest at stipulated periods

c. The total amount (Principal+ Interest) that a bond would pay

d. Yield to maturity of the bond

Ans - b

**=**16.8%