Question

You are 20 years old and have completed your BBA and want to pursue further education but you don’t want to take money from your father. Your plan is to start working and earn enough money so that you can finance your degree on your own and get yourself enrolled in five years’ time. You estimate that the annual cost of doing an MBA 5 years from today will be PKR 400,000 and the program will be two years long. You will need the money at the beginning your program so that you are not worried about how to clear your dues during your studies. Luckily you go for a job interview and they hire you and you start working at a salary of PKR 25,000. So you decide that 50% you will deposit in a saving account at a 10% rate with monthly compounding for your further studies and the remaining amount you will use for your daily expenses.

1. Will you be able to meet your goal at this current saving rate?
2. What percentage of your salary should you save if you want to have exactly your university expenses amount?
3. How would your answer to part 1 change if the saving account rate changed to 5%? Comment on your answer.

      4. If you are given an option to invest at the 10% saving rate with monthly compounding or 10.5% semiannual compounding, which would you chose? Explain your answer.

Important note: *kindly do make sure that you have read the question properly because there is a confusion in question regarding Its 2 years MBA or 5 years MBA. The calculation is based on the time period of MBA program*.

Answer 1

Salary = 25000/month

Amount deposited in savings (P) = 12500/month

rate of interest (r) = 10% = 10/100 = 0.1

n = 12 (since interest compounded monthly)

t = 5 years

The maturity value of the total investment after 5 years (60 months) given below -

[{P*(1+r/n)^(nt)} - P]/(r/n)

= [12500*{(1+.1/12)^(12*5)} - 12500]/ (.1/12

= [{12500*(1.008)^60} - 12500]/.008

=(20162.39- 12500)/.008 = 957798

Total maturity after 5 years = 957798 which is greater than 400000. Therefore, his goal will be achieved.

Now to have exact amount of A1 = 400000 after 5 years, let us assume he deposits P1 evry month.

Therefore, we now have -

A1 = {P1*(1+r/n)^(nt) - P1}/(r/n)

or, 400000 = [P1*{(1+.1/12)^(12*5)} - P1]/(.1/12)

or, 400000 = (P1*1.61 - P1)/.008

or, 400000 = (0.61*P1)/.008

or, P1 = (400000*.008)/.61

or, P1 = 5246.

Therefore, if he deposits 5246 (or (5246/25000)% = 21%), he will be able to exactly meet university expenses.

Now if savings rate changes to 5% in 1st part we have -

= [12500*{(1+.05/12)^(12*5)} - 12500]/ (.05/12)

= [{12500*1.28} - 12500]/.004

=(16042- 12500)/.004 = 850076

If rate changes to 5%, he will be still able to generate savings more than university expenses, although the total maturity will get lowered.

Now, if we have 10.5% semi annual compounding we get P = 12500*6 = 75000

= [75000*{(1+.105/2)^(2*5)} - 75000]/ (.105/2)

= 50107.2/.0525

=954423

10% monthly compounding generates 957798 in 5 years.

10.5% semiannual compounding generates 954423.in 5 years which is less.

I would choose the 1st option of 10% monthly compounding.