**Instructions to students: All questions are compulsory**

**Materials:**

Dictionaries are not permitted.

## TASK : BS1003 Financial Mathematics & Business Statistics Assignment

**Question 1**

a)A friend has received an inheritance of £40,000 and has decided to spend £5,000 now and invest the rest until he completes his medical training in six years’ time. He has been offered two different investments, and has asked you to identify the best choice. The first investment accrues quarterly interest at a rate of 6% p.a., while the second will pay £54,000 at the end of the six years.

i)Calculate the total interest your friend will earn if he chooses the first investment option. **(1.5 marks)**

ii)Calculate the annual interest rate that is being offered by the second investment. **(1.5 marks)**

iii)Which of the two investment should your friend take? Why?**(1 mark)**

b)A University is looking to replace the audiovisual equipment in three of its lecture halls. The new equipment, which will cost £250,000, is believed to have a useful life of five years, after which it is expected to have a salvage value of £20,000.

i)Calculate the annual depreciation using the linear method.**(2 marks)**

ii)Calculate the value of the equipment after 3 years, using the reducing-balance method, with a 30% p.a. depreciation rate.**(3 marks)**

c)What is the present value of a 3-year monthly annuity of £250, if the interest rate applied is 4.5% compounded monthly?**(4 marks)**

d)Your medical student friend, from question 1 above, has contacted you again, as he is entering a partnership with a local retailer in one of two investment projects. Your friend’s money would fund 25% of the initial investment for either of the projects. The cash flows generated by the projects are summarised in the table below:

- If the company’s discount rate is 9%, which project should be chosen, and why? (
**5 marks)** - What is the internal rate of return (IRR) from the Stall at a major event?
**(2 marks) (Total 20 marks)**

**Question 2: BS1003 Financial Mathematics & Business Statistics Assignment-City, University of London**

a)A law firm has been tracking the number of successful resolutions over the last six months. The data collected indicates that each partner finishes on average 8 cases per month, 5 of which with successful (win) outcomes.

i)Identify which probability distribution best describes a successful outcome, and explain the reasons for your choice.**(2 marks)**

ii)Calculate the probability that one single partner will conclude 12 cases with wins in a two-month period.**(2 marks)**

iii)Calculate the probability that another single partner will conclude 30 cases in a three-month period.**(2 marks)**

b)A production facility has been experiencing a significant number of breakdowns in the last two months. The management of the facility believes this is related to poor quality of one of the parts used in the production process, and has decided to investigate. The part is received in batches of 1,000, which have shown historically to have an average of 5 defective parts per batch with a standard deviation of 4.84. The management of the facility believes a defective rate over 0.75% would lead to breakdowns.

i)Without calculations, do you believe the identified part is the cause of the breakdowns? Why?**(1 mark)**

ii)Calculate a 95% confidence interval for the number of defectives per batch 1,000 for the part, assuming a sample of 60 parts is taken from the batch.**(2 marks)**

iii)Calculate the probability that a sample of 60 parts taken from a batch of 1,000 parts will have a percentage of defectives over 0.75%.**(2 marks)**

iv)Indicate whether you believe the breakdowns have been caused by this part, as indicated by the management of the production facility and justify.**(1 mark)**

c)A company that supplies plastic cases for DVDs is assessing whether to implement a new manufacturing process, which it believes will reduce the level of defective cases produced. In order to judge whether to go ahead with the change, the company is evaluating the current costs of returns by its customers due to defective cases. The supplier sells boxes of 1,500 cases. It knows that its customers test a sample of 45 cases and if two or more are found to be defective, the batch is returned. If the retailer sells an average of 600 boxes per month, the price per box is £1,200 and the supplier believes the cases have a defective rate of 0.4%.

i)Calculate the probability that a box is returned.**(2 marks)**

ii)Calculate the expected monthly amount of refunds paid to customers.**(2 marks)**

**d)Calculate:**

i)the probability of getting two 6s, when throwing three regular dice**(1 mark)**

ii)the probability of winning a game twice when you play it 6 times, if the probability of winning the game is 15%**(1 mark)**

iii) the probability of getting 0 heads when tossing four unbiased coins**(1 mark)**

iv)the probability of drawing a non-face card from a regular pack of 52 playing cards.**(1 mark)(Total 20 marks)**

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