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]

Salary is monthly and MBA cost is for one year as annual cost means one year cost

Answer 1

Answer :

Part 1. At a salary of PKR 25,000 and deciding that 50% you will deposit in a saving account at a 10% rate with monthly compounding for your further studies, time is 5 years

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

Answer : The formula for compound interest is P (1 + r/n)^(nt), where P is the initial principal balance, r is the interest rate, n is the number of times interest is compounded per time period and t is the number of time periods. When we add principal amount and interest, we get total amount(A). Applying this we will get as follows :

Amount after 5 years will be = $ 9,67,963

Total amount required at the beginning of year 5 for two year education program will be equal to (present value at the beginning of year 5)

= 4,00,000 + 4,00,000*0.909 = 7,63,600

Therefore, it is clear that we will be able to meet our goal at this current saving rate.

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

Answer : We need to calculate here the amount of P, in the above formula in part 1.

Total amount we have as A = 7,63,600, n = 5 and r = 10% (A is taken from part 1, you can see the calculations there, we are taking it as A, as we need exact same amount that we require to pay for education)

A = P + I

and I = P (1 + r/n)^(nt)

Putting these values, we get P = 9,861

percentage of your salary should you save = 9,861 / 25,000 = 39.45%

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

Answer : Total amount required at the beginning of year 5 for two year education program will be equal to

= 4,00,000 + 4,00,000*0.909 = 7,63,600

Compound interest @5%, then amount at the end of 5 years will accumulate =

Amount after 5 years will be = $ 8,50,076

Therefore, it is clear that we will be able to meet our goal even at this current saving rate.

Part 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 : Amount we will receive at the end of 5 years in total, in both the alternatives will be as follows:

10% saving rate with monthly compounding = $ 9,67,963

10.5% semiannual compounding = 9,54,423

Therefore, option 1, 10% saving rate with monthly compounding, will be better.