Question

Now that you are going to save 100 €/month, you decided to save those 100€ per month in a bank account that offers a 2% interest rate compounded monthly, till the day you retire (that is to say, in 20 years). Please answer the following questions:

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 2% interest rate compounded monthly, and you continue doing so till the day you retire (that is to say, in 20 years):

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

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

3. 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)

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

Answer 1

1st case: starting of the month

Annuity value= 100 EUR

Number of compounding periods= 20 years × 12 months=> 240

Interest rate for one compounding period= 2%÷12=> 0.167%

Using annuity formuls. Calculate Future Value

I.e 100*(1+r)^n

I will have EUR 29,492.19 after 20 years.

2nd case: at the end of the month.

Annuity remains same

In this n=19

As u will not get interest on the last annuity 100 eur.

N= 12*19= 228

Interest 0.167% same as case 1

Ans i i wi have EUR 27,709.33 if investment is done at the end of the month.

As u can see the diff. Case 1 is better value.