Question

You are 20 years old and have completed your BBA and want to pursue further education but you don’t want to make 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 of 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

1. Yes, you will be able to meet your goal at this current saving rate since the Future value of the monthly savings after 5 years of PKR 967,963.40 is greater than Total MBA cost for 2 years of PKR 800,000.

2. Percentage of monthly salary to save = 41%.

3. You will still be able to meet your goal at the saving rate of 5% since the Future value of the monthly savings after 5 years of PKR 850,076.04 is greater than Total MBA cost for 2 years of PKR 800,000. Although, the Future value of the monthly savings after 5 years of PKR 967,963.40 at 10% is higher than the Future value of the monthly savings after 5 years of PKR 850,076.04 at 5% saving rate.

4. I would choose the saving rate of 10% monthly compounding. The reason is that the Future value of the monthly savings after 5 years at 10% semiannual compounding saving rate of PKR 967,963.40 is greater than the Future value of the semiannual savings after 5 years at 10.5% saving rate semiannual compounding of PKR 954,422.88 by an amount of PKR 13,540.52 (i.e. PKR 967,963.40 - PKR 954,422.88 = PKR 13,540.52).

Step-by-step explanation:

Monthly salary = PKR 25,000

Monthly savings = PKR 25,000 * 50% = PKR 12,500

Annual MBA cost = PKR 400,000

Total MBA cost for 2 years = PKR 400,000 * 2 = PKR 800,000

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

To determine this, the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:

FV = M * {[(1 + r)^n - 1] / r} ................................. (1)

Where,

FV = Future value of the monthly savings after 5 years =?

M = Monthly savings = PKR 12,500

r = Monthly interest rate = 10% / 12 = 0.10 /12 = 0.00833333333333333

n = number of months the savings will be made = 5 year * 12 months = 60

Substituting the values into equation (1), we have:

FV = 12,500 * (((1 + 0.00833333333333333)^60 - 1) / 0.00833333333333333)

FV = 12,500 * 77.4370721734302

FV = PKR 967,963.40

Yes, you will be able to meet your goal at this current saving rate since the Future value of the monthly savings after 5 years of PKR 967,963.40 is greater than Total MBA cost for 2 years of PKR 800,000.

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

To determine this, we still make use of equation (1) in part (1) above by changing Future value of the monthly savings after 5 years (FV) to PKR 800,000 while other values remains the same and solve for Monthly savings (M) after substituting the values into equation (1) follows:

800,000 = M * (((1 + 0.00833333333333333)^60 - 1) / 0.00833333333333333)

800,000 = M * 77.4370721734302

M = 800,000 / 77.4370721734302

M = PKR 10,330.97

Percentage of salary to save = M / Monthly salary = PKR 10,330.97 / PKR 25,000 = 0.41323876409392, or 41%

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

We use equation (1) is part 1, retain all the other values except r which is obtained as follows:

r = Monthly interest rate = 5% / 12 = 0.05 / 12 = 0.00416666666666667

Substituting the values into equation (1), we have:

FV = 12,500 * (((1 + 0.00416666666666667)^60 - 1) / 0.00416666666666667)

FV = 12,500 * 68.0060828408433

FV = PKR 850,076.04

You will still be able to meet your goal at the saving rate of 5% since the Future value of the monthly savings after 5 years of PKR 850,076.04 is greater than Total MBA cost for 2 years of PKR 800,000. Although, the Future value of the monthly savings after 5 years of PKR 967,963.40 at 10% is higher than the Future value of the monthly savings after 5 years of PKR 850,076.04 at 5% saving rate.

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.

From part 1 above, the Future value of the monthly savings after 5 years at 10% saving rate monthly compounding is PKR 967,963.40.

To obtain the Future value of the monthly savings after 5 years at 10.5% semiannual compounding saving rate, we use equation (1) with changes in definitions to semiannual where:

FV = Future value of the semiannual savings after 5 years =?

M = Semiannual total savings = Monthly saving * 6 months = PKR 12,500 * 6 = PKR 75,000

r = Semiannual interest rate = 10.5% / 2 = 0.105 / 2 = 0.0525

n = number of semiannual the savings will be made = 5 year * 2 semiannuals = 10 semiannuals

Substituting the values into equation (1), we have:

FV = 75,000 * (((1 + 0.0525)^10 - 1) / 0.0525)

FV = 75,000 * 12.7256383972991

FV = PKR 954,422.88

Therefore, I would choose the saving rate of 10% monthly compounding.

The reason is that the Future value of the monthly savings after 5 years at 10% semiannual compounding saving rate of PKR 967,963.40 is greater than the Future value of the semiannual savings after 5 years at 10.5% saving rate semiannual compounding of PKR 954,422.88 by an amount of PKR 13,540.52 (i.e. PKR 967,963.40 - PKR 954,422.88 = PKR 13,540.52).