Question

(d) Geoffrey believes that the overall benefit from this agreement amounts to $328.18083575068 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 $328.18083575068, calculate the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly. answer is 10.72

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 $1289.5239111457 per month in advance for the coming 5 years.

(a) If Gillian can borrow/invest money at a rate of 3.6% 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"?

Please help with just part a and b. Part d is the the previouse section

Answer 1

Part (a)

Rate = interest rate per month = (1 + 3.6%)^1/12 - 1 = 0.2952%

Annuities are at the beginning of the month. Hence, type = 1.

the equivalent amount today of her future liabilities = - PV (Rate, Nper, PMT, FV, Type) = - PV (0.2952%, 12 x 51289.5239111457, 0, 1) = $ 71,021.00

Part (b)

Interest rate per month = Rate (nper, PMT, PV, FV, 1) = Rate (5 x 12, 1289.5239111457, -66000, 0, 1) = 0.5560%

Hence, the interest rate, expressed as an effective annual rate = (1 + r)¹² - 1 = (1 + 0.5560%)¹² - 1 = 6.8800%