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 $64,000 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 3.2% p.a. effective.

(a) Calculate the size of the level quarterly repayment.

(b) How much money does Geoffrey owe on this loan after 1 year?

(c) How much interest does Geoffrey pay in the first year?

(d) Geoffrey believes that the overall benefit from this agreement amounts to $320.34696082538 per week in arrears (this would include money he would have spent on alternative delivery services, estimated additional profits from using Gillian's services, etc). By considering only the initial cost of $64,000 and this weekly benefit of $320.34696082538, calculate the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly.

Answer 1

e). PV = 64,000; N = 5*4 = 20; rate (quarterly rate) = 3.2%/4 =0.800%; Type = 0 (or End), solve for PMT.

Quarterly repayment amount = 3,475.58

f). Principal owed after one year: PV = -64,000; PMT = 3,475.58; N = 4; rate = 0.008%, solve for FV.

Principal owed after one year = 52,002.67

Total amount owed after one year = PMT*(number of total repayments*repayments made)

= 3,475.58*(20-4) = 55,609.27

(Note: The question does not clarify whether principal outstanding or net amount outstanding after one year is asked for, so both have been calculated.)

g). Interest paid in one year = (PMT*4) - principal paid in one year

= (3,475.58*4) - (64,000-52,002.67) = 1,904.99

h). PV = -64,000; PMT = 320.34696082538 ; N (number of weeks in 5 years) = 5*52 = 260, solve for RATE.

Weekly rate = 0.2117%, so

nominal annual rate = weekly rate*number of weeks in a year = 0.2117%*52 = 11.01%