Question

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

a) Given starting debt = $5000

Given Interest compounded semi annually = 18.5%

Therefore, interest charges every six months = 9.25%

Payment every month is = 3%

Therefore, payment every 6 months is = 18%

Payment made for 6 months is constant as it is based on the starting amount, whereas interest paid every 6 months changes based on the remaining amount.

In the table below payment made for 6 months and interest paid every 6 months is shown. Interest is 9.25% of the beginning amount and Payment is always 18% of $5000. It takes 8 half year terms plus one month (remaining $131.13) to complete all the payments. Which is 8 x 6 + 1 = 49 months

	Begning Amount	Payment	Interest	End Amount
1	5000.0	900	462.5	4562.5
2	4562.5	900	422.0	4084.53
3	4084.5	900	377.8	3562.35
4	3562.4	900	329.5	2991.87
5	2991.9	900	276.7	2368.62
6	2368.6	900	219.1	1687.71
7	1687.7	900	156.1	943.83
8	943.8	900	87.3	131.13

b)

Present value of investment that yields C till perpetuity at the rate R% = C/R

Therefore lumpsome investment in this case is = 3000/5%

Single lumpsome investment = $60,000

c)

#1 Effective rate of interest for Continuously compounding = (e^rt - 1) x 100= (e^0.0495-1) x 100 = 5.07%

#2 Effective rate of interest for monthly compounding is

= 5.12%

Therefore taking loan with #1 option is better