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.

Answer 1

Answer:

1. Will you be able to meet your goal at this current saving rate?

• yes, you will even have some spare money

annual cost of MBA = 400,000 x 2 years = 800,000

monthly salary = 25,000 and you will deposit 12,500

ordinary annuity, 0.8333%, 59 periods (5 years - 1 month) = 75.80535

the future value of your account = 12,500 x 75.80535 = 947,566.88 which is more than the cost of the MBA

2. What percentage of your salary should you save if you want to have exactly your university expenses amount?

• 42.2138%

800,000 / 75.80535 = 10,553.34

10,553.34 / 25,000 = 0.422138 = 42.2138%

3. How would your answer to part 1 change if the saving account rate changed to 5%?

• actually you still have more money than what you need even if the interest rate falls to 5%, so you can still take your MBA

monthly salary = 25,000 and you will deposit 12,500

ordinary annuity, 0.41666%, 59 periods (5 years - 1 month) = 66.72805

the future value of your account = 12,500 x 66.72805 = 834,100.63 which is more than the cost of the MBA

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?

• I would choose the 10.5% semiannual compounding because the effective interest rate is higher.

the effective interest rate of investing at 10% compounded monthly = (1 + 10%/12)¹² - 1 = 10.47%

the effective interest rate of investing at 10.5% compounded semiannually = (1 + 10.5%/2)² - 1 = 10.77%