Question

Question 5 - 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 $66,000 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 4.3% p.a. effective. (a) Calculate the size of the level quarterly repayment.

Question 6 - (b) How much money does Geoffrey owe on this loan after 1 year?

Question 7 - (c) How much interest does Geoffrey pay in the first year

Question 8 - (d) Geoffrey believes that the overall benefit from this agreement amounts to $313.62126244401 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 $66,000 and this weekly benefit of $313.62126244401, calculate the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly.

Question 9 - A) 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 $1371.7057354746 per month in advance for the coming 5 years. If Gillian can borrow/invest money at a rate of 3.8% 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.

Question 10 - (b) The money she receives from Geoffrey can be considered a loan ($66000), 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

1. Given principal amount =$66000

interest rate per year = 4.3% so per quarter = 4.3/4=1.075%=r

No of years of loan= 5 years or 5*4=20 quarters =n

so Equated quaterly payment = E=P*r*(1+r)^n/((1+r)^n-1))

so P is the loan amont

so E= (66000*1.075%*(1+1.075%)^20)/((1+1.075%)^20-1)

= E= 3685.09

2. one year of payment i,e= 3685.09*4=14740.36$

Total amount to be paid =3685.09*20=73701.81$

So amount owed after one year of repayment= $58961.44

3.Interest paid in the first year

quarterly payment	Interest amount	Principal repaid	Loan balance
3685.09	=66000*1.075%=709.5$	=3685.09-709.5$=2975.59	=66000-2975.59=63024
3685.09	=63024*1.075%=677.15$	=3685.09-677.15$=3007.557	=63024-3007.557=60016
3685.09	=60016*1.075%=645.18$	=3685.09-645.18=3039.91	56976.92$
3685.09	=56976.92*1.075%-612.5$	=3685.09-612.5$=3072.59	=56976.92-3072.59=53904.33$
total	2644.692$

so in the first year he has paid 2644.692$

4 Weekly he receives benefit of 313.62126244401$

Taking this as weekly income

= rate at which 313.62126244401$ will become 66000$

so 66000=sumof all present value of 313.62126244401$ received for 5 years

So by using excel we can find that 0.68% per week is the interest rate i,e 0.68%*52 weeks is 35.36 %