Question

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 $1535.1190329477 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

a. The computation of the today equivalent amount is given below:

Here we find the present value by using the excel spreadsheet

Mentioned that

Rate = 3.5% / 12 = 0.2916666%

NPER = 5 *12 = 60

PMT = $1535.1190329477

FV = $0

Now using the present value formula which is given below:

PV = -(RATE,NPER, PMT, FV, 0)

After applying the above formula,

The today equivalent amount is $84,385.48

b.The effective interest rate is

Effective annual rate = [ 1 + (interest rate / number of months) ]^{number of months} - 1

= [1 + (0.035/12) ]¹² - 1

= (1+ 0.002916)¹² - 1

= (1.002916¹² - 1

= 1.035567 - 1

= 3.5%