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 $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 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 $313.69415778668 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 $313.69415778668, calculate the interest rate that represents the return on this investment, expressed as a nominal annual rate compounding weekly.

Answers to previous questions (might help)

present value of running costs : $39767.70

present value of sale price : $7047.83

total cost of buying and running a car : $65719.87

equielent monthly repayment over next 5 years : $1186.75

Answer 1

a)

The Computation of Equated Quarterly Payments will be  

P - is the Principal = 66,000

R- Rate of interest = 3.2% p.a or 0.8% per Quarter or 0.008

n- Number of Installments = 20 (4 quarterly installments for 5 years)

                                                                                                                                                    

                                                                          

    

b) amount owed by G at the end of Year 1 is $53,627.75 as per the amortization Table Below

The closing Balance at year 1-in the above table is highlighted in green color.

From the quarterly payment of 3584.19- interest Portion @ 0.8% per quarter on the opening Principal outstanding amount is computed and reduced to Arrive at the principal Portion. This principal is reduced from the opening Principal outstanding to arrive at the closing Principal outstanding at every quarter.

the excel formula are

C   The amount of interest paid by G in the first year is highlighted in Yellow Color in the above table and the total of the same works out to $ 1,964.52

D)    the Nominal Annual Rate compounded Annually works out to 6.14%

We Know,

P X (1+r)ⁿ = Future Value ofCash Flows

Principal - is the initial investment of 66000. n = Number of weeks in 5 years=5*52 or 260 weeks

Future cash flows =313.69415778668 per week X 260 weeks

Substituting we get

66000 X ( 1+r)²⁶⁰ = 313.69415778668 X 260

   ( 1+r)²⁶⁰ = 81560.48 / 66000

                          = 1.35934135040895

             1+r       = 1.00118146769628

                r        = 0.00118146769628     or       0.118146769628 %

     This is the compounded rate per week, so Compounded yearly rate will be   0.118146769628 X 52

                        = 6.14%