Question

You decided to quit smoking today.

Now that you are going to save 300 €/month, you decided to save those 300€ 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​​​​​​​​​(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 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) 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 0.2% 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​​​​​​​​​​​​​​​​​​​(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)

Answer 1

soll 0.416776 Po monthly installment darmthly Rete z 50% ne20x12' Tż 240 Maths. Ta hand o M-2 M-2 M3 M4 MB 300 300 3001 300 300 - bol total cashflows are 24O. US equal to Number of 4 months. I - Cos Money at the end o n out - A G P 1 = (148) 3 300x71- (1+0.004167) 0.004167 E 300 x 1515202 ci 35,456 , 06 Paesent velice _ 240 X (1,00416320 (123315.76 future Value

(210) 0 Ml M.2 M.3 309 300 300 300 M-4 M.5 300 300 Parsent vame of annuity Que =Px 1- (142) JxC1+7) -240 309x 1-(1.004167) 7x 6 0004167 (19046 300 x 1520 1516 - = 45,645.49 Present veue I 9 X (1,0041677240 (future vane.) Tu 123,829.66 Y (bal here the main difference will be the interest date of flest month why in first case we have started deposite at the end of first month whre in this case we have streut it at the begining of each month so We will have fiast month's interest over the amount in Q. 10 (6 obviouly the begining of the ronth deposites are much better because it will halte one month additinde Interest . as discussed above

Go timeline - o A.1 300 m 2 Mp3 M-4 M-5 309,61301.201851.80 (302,40. +9 Poesent 1 Value At of growing = Ronanpuity 240 = 300 0.002167-0.002 17/ 1002 le OOH162 bis 300 x 360 233 kB na 220,870.8861 Besent value 240p God blix (\00 4167) - Sgg, 190.gg Hoopst notre growth rate the amount we be infinite. because in lauwland ProDoo ! C0-99

I hope my efforts will be fruitful to you.?