Question

Geoffrey is the owner of a small grocery store and is considering buying a car to help him transport his wares. He has found a suitable used car online that he was able to negotiate to a price of $40,000. After doing a bit more research, he has found the following additional expenses involved in the purchase:

• Insurance and registration will cost $510 per year, payable at the start of each year

• Based on mileage estimates, petrol will cost $220 per fortnight, payable at the end of each fortnight

• Servicing will cost $380 per year, payable at the end of each year (as the car was recently serviced by the previous owner

Assume that these are the only expenses involved with the purchase and operation of the car.

Geoffrey believes that the car can be used for 5 years before it will no longer be reliable, at which point he expects to sell it for a quarter of its current purchase price. He also has a business account at the bank that lets him borrow or invest money at 4.6% per annum effective.

Now 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 $80,000 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 4.6% p.a. effective.

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

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

show working out please

Answer 1

Quarterly rate equivalent to Effective Annual Rate of 4.6% = (1+4.6%)^(1/4)-1 = 1.130679%

Level quarterly payment is $4,491.78

(a ): Amount that owe after one year= $65,405.86

(b ): Interest that pays in one year= $3,372.97

Calculations as below: