Question

Q. 6

Each of the questions below is INDEPENDENT of the other.

(Timelines are not required.)

(a) Your sister has a $5,000 debt balance on her credit card that charges 18.5% interest compounded semi-annually. The monthly payment is 3% of the starting debt balance.

Required:

If your sister stops using the credit card for purchases, how many months (round up) will it take her to pay off the credit card balance? (Timeline not required.)

(b) Your high school guidance counsellor encouraged you to follow your dream and learn a trade following high school. You became a licensed mechanic, opened your own shop which later franchised and you became independently wealthy. You decided to create a bursary at the high school to be given to a student planning to pursue a trade following high school. You want to give a lump sum amount that would generate a $3,000 bursary per year into perpetuity.

Required:

Assuming an investment rate of 5%, how large must the lump sum amount be?

(c) Your Aunt asks for your help in deciding on a Bank Loan.

Bank Loan # 1 charges 4.95% compounded continuously.

Bank Loan # 2 charges 5.0% compounded monthly.

Required:

Which Bank Loan would you recommend to your Aunt, and why?

(Show all calculations to support your answer.)

Answer 1

Q#(a):

Equivalent monthly rate of 18.5% compounded semi annually is 1.485402% as follows:

Given, monthly payment= 3% of starting debt balance

=$5,000*3%= $150.

Number of months required to pay off the debt= 47 (Rounded up)

Calculation as below:

Q#(b):

Present value of perpetuity= C/r

Where

C= Periodical payment (given as $3,000) and r= Interest rate (given as 5%)

Plugging the inputs,

Lump sum amount to be given (PV of perpetuity)= 3000/0.05 = $60,000

Q#(c):

Given, Interest rate of Bank Loan #1= 4.95% compounded continuously

Effective annual Rate (EAR)= e^r-1

Where

e= constant 2.71828, r= interest rate (given as 4.95%)

EAR= 2.71828^0.0495 = 5.074556%

Bank Loan #2 Interest rate= 5% compounded monthly.

EAR= (1+r/12)^12-1 = 1.004166667^12-1

= 1.0511619-1= 5.11619%

This shows that Bank loan #1 has lower effective interest rate and hence the same is opted.