Business Math for CAIIB IIIBusiness Math for CAIIB III

Objective QuestionsObjective Questions

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Ravindra A. KamathRavindra A. Kamath

• How much will Rs.80,000 amount to in 2 years, at compound interest, if the rates for the successive years are 12% and 15%?

• (a) Rs.97,600 (b) Rs.1,04,440

• (c) Rs.1,03,040 (d) Rs.24,440

• The compound interest on a sum of money for 2 years is Rs.880 and the simple interest on the same sum for the same period & at the same rate of interest is Rs.800. What is the sum?

• (a) Rs. 4,000 (b) Rs. 1,000

• (c) Rs. 2,400 (d) Rs. 2,000

• The C.I, compounded annually, on an investment for the second year is Rs.2420 and for the third year is Rs.2662. What is the principal invested?

• (a) Rs.22,000 (b) Rs.2,000

• (c) Rs.20,000 (d) Rs.2,400

• How long will it take a sum of money to become 6 times if it is invested at 12% p.a. C.I.?

• (a) 12 years (b) 16years

• (c) 18 years (d) 36 years

• When a certain sum of money is invested for a certain time at 8% p.a. simple interest, it amounts to Rs.200. If the same principal is invested for the same duration at 10% p.a simple interest, it amounts to Rs.212.50. What is the duration for which it was invested?

• (a) 5 yrs 4 months (b) 3 yrs 9 month• (c) 4 yrs 2 months (d) None

• A certain sum of money invested at compound interest earns an interest of Rs.630 at the end of two years and Rs.993 at the end of three years. What is the rate of interest?

• (a) 10% (b) 20%

• (c) 15% (d) None.

• Mr. Navin invested in a bond at C. M. P. of Rs. 970/- If Face Value is Rs. 1000, Maturity Period is 5 years and coupon rate is 9% p.a. What is his Y.T.M.?

• a. 9.50% b. 9.25%

• c. 9.75% d. 10%

• Mr. Modi wants to sell a bond of Face Value Rs. 10000/- with coupon rate 11% & maturity period 6 years. At what price he should sell it if market rate is 10%?

• a. below Rs. 10435/-

• b. below Rs. 10,300/-

• c. above Rs. 10435/-

• d. above Rs. 10,300/-

• Calculate the I.R. R. of a project with C. F’s as under:

0 yr. – 1,000,000;1yr. 200,0002 yr. 400,0003 yr. 600,000• a. 8.25% b. 8.00%• c. 8.50% d. 7.50%

• Calculate the NPV of a project with FCFs as above and capital cost is 15% p.a.

• a. 870880

• b. 120120

• c. 130120

• d. -129120

• Calculate the Average rate of returns for the above FCF’s

• a. 13.00%

• b. 13.35%

• c. 13.50%

• d. 13.75%

• Current Price of a share is Rs. 100. The economic state is as follows

Economy Probability Price Growth 0.6 130Recession 0.4 90Calculate the expected return for the stock?• a. 10% b. 15%• c. 14% d. 16%

• In theory of Sampling “ the larger the size of the sample the greater the accuracy” is based on:

a. law of Statistical regularity

b. law of Inertia of large numbers

c. law of Statistical imperfection

d. law of large numbers

If P = 0.5 Q = 0.5σ = 0.05Find the sample sizea) 1000b) 100,000c) 100d) 10,000

• Compute the risk associated with Apex Ltd, having the following probability distribution:

Return (ki) 7% 6% 7.89% 5.6%

Probability (Pi)0.20 0.30 0.40 0.10

Weighted average returns for Apex Ltd. is:

a) 6.916% b) 7.852%

b) c) 5.906% d) 6.508%

• Compute the risk associated with Apex Ltd, having the following probability distribution:

Return (ki) 7% 6% 7.89% 5.6%

Probability (Pi)0.20 0.30 0.40 0.10

What is the standard deviation of the returns?

a) 2.29% b) 0.898%

b) c) 1.145% d) 1.694%

• Compute the risk associated with Apex Ltd, having the following probability distribution:

Return (ki) 7% 6% 7.89% 5.6%

Probability (Pi)0.20 0.30 0.40 0.10

What is the range of the returns?

a) 1.40% b) 1.290%

c) 2.29% d) .89%

• Compute the risk associated with Apex Ltd, having the following probability distribution:

Return (ki) 7% 6% 7.89% 5.6%

Probability (Pi)0.20 0.30 0.40 0.10

What is the coefficient of variation for this data?

a) 1.34 b) .547

c) .630 d) .1298

• The following are the data on a capital project being evaluated by the management of X Ltd.,

• Project M: Annual cost saving Rs.40,000, • Useful life 4 years• I.R.R. 15% Profitability Index • (PI) 1,064• Salvage value 0Considering the following table of discount factors:

15% 14% 13% 12%1 Year 0.869 0.877 0.885 0.8932 Year 0.756 0.769 0.783 0.7973 Year 0.658 0.675 0.693 0.7124 Year 0.572 0.592 0.613 0.636

• The Pay back period of Project of Project M is:

• a) 2 year 11 months

• b) 2 years 9 months

• c) 2 years 12 months

• d) None of the above

• What is the cost of capital of Project M

• a) 12%

• b) 14%

• c) 16%

• d) 18%

• Project-M’s NPV is:

• a) 7,211

• b) 7,309

• c) 8,014

• d) 8,020

• Cost of Project M is:

• a) 1,14,600 b) 1,14,200

• c) 1,14,860 d) 1,14,940

• A company manufactures Radios (x) and Tape recorders (y). Cost of making radio & tape recorder is Rs. 225 and Rs. 375 respectively. The company works in 2 shift totaling 14 hrs. The production and assembly time for a radio is 2hrs while that for tape recorder is 3 hrs. The radio sells for Rs.250 while the tape recorder sells for Rs.410. The company spends an amount of Rs. 75,000 per day on production. Maximize the production in terms of optimum number of radios and tape recorders. Pick the correct constraint equation from the choice given against each type.

• Capacity constraint (machine time)

• a) 3x + 2y ≤ 14 b) 2x + 3y ≤ 14

• c) 2x + 3y ≥14 d) 3x + 2y ≥14

• Financial constraint (amount available)

• a) 250x + 410y ≤ 75000

• b) 3x + 5y ≤ 75000

• c) 3x + 5y ≤ 1000

• d) 3x + 5y ≥ 1000

• Non – negativity (minimum number)

• a) x > 0 ; y > 0

• b) x = 0 ; y = 0

• c) x ≤ 0 ; y ≤ 0

• d) a & b

• Objective function (to maximize profit)

• a) P = 25x + 35y

• b) P = 20x + 35y

• c) P = 25x + 30y

• d) P = 20x + 35y

• A firm makes chairs (x) and tables (y). Each table costs Rs.400 in material and Rs.150 in labor. Each chair costs Rs.175 in material and Rs.75 in labor. The price of table and chair is Rs.625 and Rs. 300 respectively. The firm has 12 hours of time per day. The production time for each table and chair is 4 hrs, 1.5 hrs respectively. The firm has liquidity of Rs.7000 per day to pay for the material and labor. The objective is to maximize the production for the firm by optimizing the production of tables and chairs. Pick out the correct option for each of the constraint equation.

• Capacity constraint (machine time)

• a) 4x + 1.5y ≤ 12

• b) 1.5x + 4y ≤ 12

• c) 4x + 1.5y ≥ 12

• d) 1.5x + 4y ≥ 12

• Financial constraint (amount available)

• a) 5x + 11y ≤ 14000

• b) 5x + 11y ≥ 700

• c) 12x + 25y ≤ 7000

• d) 12x + 25y ≥ 7000

• Non – negativity (minimum number)

• a) x ≥ 0 ; y ≥ 0

• b) x = 0 ; y = 0

• c) x < 0 ; y < 0

• d) b & c

• Objective function  (To maximize profit)

• a) P = 75x + 50y

• b) P = 50x + 75y

• c) P = 55x + 75y

• d) P = 75x + 50y

Which of the following is a method of Which of the following is a method of selecting samples from a population?selecting samples from a population?

a) Judgement sampling a) Judgement sampling

b) Random sampling b) Random sampling

c) Probability sampling c) Probability sampling

d) All of the above d) All of the above

Suppose that a population with N=144 has Suppose that a population with N=144 has µ=24.What is the mean of the sampling µ=24.What is the mean of the sampling distribution of the mean for samples of distribution of the mean for samples of size 25?size 25?

a) 24 a) 24

b) 2 b) 2

c) 4.8 c) 4.8

d) Cannot be determinedd) Cannot be determined

Determine the sample size if standard Determine the sample size if standard deviation is 6,population mean is 25 and deviation is 6,population mean is 25 and sample mean is 23.The desired degree of sample mean is 23.The desired degree of precision is 99%.precision is 99%.

a)60 b) 75 c) 90 d) 45a)60 b) 75 c) 90 d) 45

A sample size of 90 values has a mean 55 A sample size of 90 values has a mean 55 and standard deviation 3.A second sample and standard deviation 3.A second sample of 110 values has mean 60 and standard of 110 values has mean 60 and standard deviation 2.Find the mean and standard deviation 2.Find the mean and standard deviation of the combined sample of 200 deviation of the combined sample of 200 values.values.

a) 54.5;2.812 a) 54.5;2.812 b) 62;4.345 b) 62;4.345

c) 57.75;3.526c) 57.75;3.526 d) 61.90;3.89d) 61.90;3.89

Light bulbs are manufactured in a factory Light bulbs are manufactured in a factory and have a mean life of 540 hours and and have a mean life of 540 hours and std.deviation of 50 hours.Calculate the std.deviation of 50 hours.Calculate the fraction of bulbs that have less than 500 fraction of bulbs that have less than 500 hours.hours.

a)0.54 b)0.2119 c)0.4234 d)0.3555a)0.54 b)0.2119 c)0.4234 d)0.3555

• Light bulbs are manufactured in a factory Light bulbs are manufactured in a factory and have a mean life of 540 hours and and have a mean life of 540 hours and std.deviation of 50 hours.Calculate The std.deviation of 50 hours.Calculate The fraction of bulbs having life betweenfraction of bulbs having life between

500 to 600 hours.500 to 600 hours.

a) 0.6730 b) 0.5478 c) 0.7734 d) 0.3487a) 0.6730 b) 0.5478 c) 0.7734 d) 0.3487

The mean and standard deviation of The mean and standard deviation of marks of students of a class are 55 and 8 marks of students of a class are 55 and 8 respectively. Within what interval centred respectively. Within what interval centred around the mean do at least 90% of marks around the mean do at least 90% of marks lie?lie?

a)40 and 65 b)39 and 61 a)40 and 65 b)39 and 61

c)42 and 68c)42 and 68 d)30 and 72 d)30 and 72

A binomial distribution has n=20 and A binomial distribution has n=20 and p=0.3.Find the mean and the variance of p=0.3.Find the mean and the variance of the distribution.the distribution.

a) 8 and 3.4 a) 8 and 3.4 b)4 and 2.6 b)4 and 2.6

c) 6 and 4.2 c) 6 and 4.2 d)12 and 4.4d)12 and 4.4