# Mathematics

BCO126 Mathematics of Finance Task brief & rubrics

You are asked to answer all the questions in the proposed case.

This task assesses the following learning outcomes:

· Assess the present value of future cash flows and the future value of regular savings, annually and periodically.

· Understand the annuity valuation and their factors – annual and periodical – and with various starting dates with and without growth.

· Demonstrate an ability to apply the technical skills in a practical context.

LAUNCH: WEEK 10 / DELIVERY: APRIL 24th, 2020, 23:59HRS ON MOODLE

Submission file format: Word document with all the answers, clearly identifying all steps, results, and including comments besides each answer.

You decided to quit eating junk food today.

Now that you are going to save 325 €/month, you decided to save those 325€ per month in a bank account that offers a 5% interest rate compounded monthly, till the day you retire (that is to say, in 30 years). Please answer the following questions:

1. If you do your deposits at the end of every month (so your first deposit will be in one month from today) in a bank account that offers a 5% interest rate compounded monthly, and you continue doing so till the day you retire (that is to say, in 30 years):

a) Draw the timeline (at least the first five periods) with its corresponding numeration of periods and cashflows in their corresponding points (10 points)

b) How many cashflows will be there? (10 points)

c) how much money will you have at the end? Show the workout (10 points)

2. If you decide to do your deposits at the beginning of every month (so your first deposit will be done today) in a bank account that offers a 5% interest rate compounded monthly, and you continue doing so till the day you retire (that is to say, in 30 years):

a) Draw the timeline (at least the first five periods) with its corresponding numeration of periods and cashflows in their corresponding points (10 points)

b) What is the difference between this case and the previous one? (10 points)

c) According to your opinion, what is it better? To bring the amounts to the bank at the beginning of every month (as described in this ex.) or at the end of every month (as described in the previous ex.)? Explain the reason (10 points)

d) How much money will you have at the end? Show the workout (10 points)

3. If you decide to do your deposits at the end of every month (similarly to ex.1, so your first deposit will be in one month from today) in a bank account that offers a 5% interest rate compounded monthly, and the deposits will increase in a 0.25% month after month, and you keep on doing so for the next 30 years:

a) Draw the timeline (at least the first five periods) with its corresponding numeration of periods and cashflows in their corresponding points (10 points)

b) how much money will you have at the end? Show the workout (10 points)

c) What would it happen if the growth rate and the interest rate is the same? (10 points)

Rubrics

 100 Points Descriptor 40% The student demonstrates understands the concepts and uses the right approach with the right formulas 10% The student explains the calculations, and which is the theory behind 35% The student applies the right numbers in the formulas 10% The student finds the right answer 5% The student shows an accurate presentation

Points are at the end of each question.

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