Question

Q4.      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 marks]
2. What percentage of your salary should you save if you want to have exactly your university expenses amount? [2 marks]
3. How would your answer to part 1 change if the saving account rate changed to 5%? Comment on your answer. [2 marks]
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. [4 marks]

Answer 1

EAR = (1+(r/n))^n - 1

EAR = (1+(10%/12))^12 - 1

EAR = 10.47%

Amount required in 5years=400000+(400000/(1+10.47%)) (future value = present value / (1+r)^n )

= 762,084.97

1)

Future value of annuity = P*[(1+r)^n - 1 / r ]

P = monthly savings = 25000 / 2 = 12500

r = monthly interest rate = 10%/12 = 0.83%

n = number of periods = 60

Future value = 12500*[(1+0.83%)^60 - 1 / 0.83%]

Future value = $967,963.40

Future savings exceeds required amount so answer is yes we will be able to meet the goal at current saving rate

2)

We need to find 'P' using above formula

762,084.97 = P*[(1+0.83%)^60 - 1 / 0.83% ]

P = 9841.35

So percentage savingsrequired=(9841.35/25000)=39.37%

3)

When savings account rate changed to 5%

Monthly rate = 5%/12 = 0.42%

Future value = 12500*[(1+0.42%)^60 - 1 / 0.42% ]

Future value = $850,076.04

Still we will be able to meet future requirements,even though when compare to 1 future value is lesser

4)

We should choose 10.5% with semi annual compounding

Because EAR of 10% with monthly compounding is 10.47% (calculated above)

EAR Of 10.5% with semi annual compounding is

= (1+(10.5%/2))^2 - 1

= 10.78%

Semi annual compounding with 10.5% has high EAR

(in case of any further explanation please comment)