Question

You decided to quit smoking today.

Now that you are going to save 100 €/month, you decided to save those 100€ per month in a bank account that offers a 5% interest rate compounded monthly, till the day you retire (that is to say, in 20 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 20 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

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 20 years):

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

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

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

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

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 0.2% month after month, and you keep on doing so for the next 20 years:

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

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

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

Answer 1

a) Timeline for the first 12 periods has been given below:

b) Total Number of Cash Flows = Number of years* Cash Flows in a year = 20*12= 240