Question

Geoffrey decides not to buy the car mentioned earlier. Instead, he is now considering a food delivery service "You, bars, meats" that his friend Gillian has recently started. Gillian has agreed that for a single payment of $70,000 today to help her launch her business, she will provide all the delivery services that Geoffrey needs for his business for the next 5 years. Geoffrey is considering borrowing the full amount from his business account. Suppose that Geoffrey makes level quarterly repayments over the coming 5 years, the first payment being exactly 3 months from today. Again, the interest rate on Geoffrey's account is 4.0% p.a. effective.

(a ): Level quarterly payment= $3,873.35

(b ): Amount that owe after one year= $57,076.10

(c ): Interest that pays in one year= $2,569.50

(d ): In repaid in weekly payments in arrears of $ 340.33579318617 over 5 years, nominal annual rate compounded weekly= 9.74%

Gillian has entered the agreement with Geoffrey described above. She estimates that the costs of the delivery services she has promised to Geoffrey (petrol, insurance, wear and tear, etc) amount to $1402.1924701853 per month in advance for the coming 5 years.

(a) If Gillian can borrow/invest money at a rate of 3.5% p.a. effective, what is the equivalent amount today of her future liabilities? Note that this calculation should not involve the payment she receives from Geoffrey today.

(b) The money she receives from Geoffrey can be considered a loan, with repayments being the value of the services she provides in return. What is the interest rate, expressed as an effective annual rate, she is being charged on this "loan"?

Answer 1