Question

1. You are thinking of buying a used car for $4,000 for driving to school. Your parents are willing to lend you the $4,000 and charge only 2.4% APR. They want the loan repaid equally in 48 monthly payments, with the first payment due at the end of the month in which you buy the car. You estimate that the monthly cost of operating the car, including gas, insurance, maintenance and licence fees will be $200 and payable at the start of each month. The cost of a monthly bus pass is $80. You expect that the car will be totally worn out in four years, with zero resale value, when you are finished school. Your discount rate is 6% compounded annually.
   1. If you have 3 roommates who also need transportation to and from school, how much do you need to charge each of them a month in order to cover all your costs? (You all plan to go to summer school, so you can assume 12 payments a year).
   2. Does it make financial sense to buy the car? Explain your answer.

Answer 1

We need to understand the problem a little before we can proceed to solve it:

• We need to calculate the monthly loan payments of the car
• We need to calculate the PV of the additional costs
• We need to calculate the total cost of the car
• We need to find the per head cost per month of the 4 roommates including yourself
• Once the per head cost per month is calculated, then we need to compare it with the bus pass cost to see whether car is profitable or not

First we find out the total cost of the car loan:

We are given the following information:

r	2.40%
n	4
frequency	12
PV	$         4,000.00

We need to solve the following equation to arrive at the required PMT

So the monthly payment is 87.48

Total payments are 48 so the total cost of car including interest is 87.48*48 =  $4,199.07

Next we need to find out the PV of the additional costs, additional costs are paid at the beginning of the month so they will be an annuity due:

We are given the following information:

PMT	200
r	6.00%
n	4
frequency	12

We need to solve the following equation to arrive at the required PV

So the PV of these costs is 8558.64

So the total cost of the car is 8558.64+4199.07 =12757.71

This needs to be divided among 4 people so per head total cost is 12757.711/4 =3189.43

Now we need to find out the monthly expense of this cost

We are given the following information:

r	6.00%
n	4
T	12
FV	$              3,189.43

We need to solve the following equation to arrive at the required PMT

So per head the monthly payment should be 58.96

a) So you need to charge each roommate $58.96 per month for transportation

b) monthly bus pass is $80 while the car cost is $58.96 so car is profitable.