Question

George and Martha have $6000 in a checking account that pays no interest. They want to buy their first car right now, and at the same time save monthly toward a house. The plan is to drive the car for 5 years, then sell it the same month they put the money down on the house. You have been asked to help them decide which car to buy and to determine, based on their plan, the highest price house they can afford to buy.

Part 1

Buying the car. They have narrowed their choice to two models, one from dealer A and one from dealer B.

  

	Car A	Car B
Price	$26,000	$21,000
Down payment	8%	15%
APR	1.5%	2.5%
Months to pay	60	48
Resale value	30%	40%
Miles/gallon	35	30

  

Cost of operating the car. In addition to their monthly car payments, G&M will need to buy gas, change the oil, and pay for insurance.  

• They assume gas will average $2.60/gallon over the next 5 years. They drive 20,000 miles each year.

• Oil changes are $60 every 5000 miles.

• Insurance and licensing fees are based on the car price, and they figure that 5% of the full price each year will suffice to cover both.

  

Calculate:

1. Monthly and total (5-yrs) payments for both car options (make sure you calculate the monthly payments only on the amount you are borrowing!)

2. Monthly and 5 year operating cost for both car options, and  

3. Total cost of ownership of each car option over the 5 years.  

4. Choose the car you think George and Martha should purchase and explain why you chose the car you did. You will use the costs of the car you chose to complete Part 2.

  

Part 2

Buying the house

• The car down payment will come from their bank account, and whatever is left will stay in the checking account as a cash reserve.  

• After all their other monthly expenses, G&M have a net positive cash flow of $1400. They will make the monthly car payments, insurance payments, gas and oil payments from their cash flow of $1400 (so monthlies can never be more than this amount).  

• Any excess cash (from the $1400) will go into a long term savings plan for 5 years that pays an APR of 6% compounded monthly.  

• At the end of the five years, they will sell the car and cash out the long term savings plan, put the amount of their original car down payment back in checking so they can shop for a new car.

• The remaining long term savings plan balance they will use as a down payment on a new house, which they expect to be 15% of the house’s price.

  

Calculate:

1. Total funds in the long term savings plan after 5 years,  

2. Funds available for a down payment on a house,  

3. Highest house price they can afford, and  

4. Monthly payment for a 30-year mortgage at 4.5% APR  

  

Part 3  

Report to George and Mary

  

Now that you have completed your calculations, it is time to create a report for George and Mary, outlining your recommendations to them. In this report you should include the following:

• The recommended car purchase, with a written justification, referencing the formulas and your calculations,

• A written explanation of how you arrived at the amount to be saved monthly, referencing the formulas and your calculations, and

• A written explanation of how you determined the most expensive house they can afford, and the monthly payment resulting from the purchase of that house.

Answer 1

	George & Martha
	Car details	Car A	CarB
a	Price	$                        26,000	$                 21,000
	Down Payment	8%	15%
b	Down Paymnet Amt $	$                          2,080	$                   3,150
	APR	1.50%	2.50%
	Monthly Interest %=i	0.125%	0.208%
	Amount to Borrow=a-b= P	$                        23,920	$                 17,850
	Months to pay =n	60	48
	Monthly Payment amount A is given by formula below
	A= [i*P*(1+i)^n]/[(1+i)^n-1]
	A =	=[0.00125*23920*(1+0.00125)^60]/[(1+0.00125)^60-1]	=[0.00208*17850*(1+0.00208)^48]/[(1+0.00208)^48-1]
	or A=	$                       414.05	$                 391.13
E	Monthly Installment paymnet amount	$                       414.05	$                 391.13
	Total Installment amount for loan	$                        24,843	$                 18,774
A	Total Installment + Down Paymnet	$                       26,923	$                 21,924
	Resale value	30%	40%
B	Resale Amount	$                          7,800	$                   8,400
c	Insurance amount @5% of Price	$                          1,300	$                   1,050
	Total Miles driven a year	20000	20000
d	Oil Change @$60 for each 5000 miles	$                             240	$                      240
	Miles per gallon	35	30
	Gallons of Gas required /year	571.43	666.67
e	Yearly Cost of Gas @$2.6/gallon	$                      1,485.7	$                1,733.3
f	Total Yearly Operaing Cost=c+d+e=	$                    3,025.71	$              3,023.33
g	Monthly Operaing cost =f/12	$                       252.14	$                 251.94
C	Total Operating cost in 5 years=5*f	$                  15,128.57	$           15,116.67
D	Total Cost of owning the car=A-B+C	$                  34,251.72	$           28,641.10
F	Monthly Installment & Operating cost payout=E+g=	$                       666.20	$                 643.08
	They should buy car B as the total cost of ownership in lesser.
	Buying House
	Balance in checking account	6000
	less - car down payment	-3150
	Remaining Balalnce in hand	2850
	Net positive cash flow	1400
	Less monthly installment and operaing cost	$                      (643.08)
	Net surplus cash in hand	$                       756.92
	They will put $756.92 each month in Long term saving plan for 60 months with
	APR 6% compounded monthly.
	Monthly Interest rate =0.5%
	Formula for future value of Ordinary Annuity :
	FV= A [ {(1+k)n-1}/k]
	FV = Future annuity value
	A = monthly investment=756.92
	K=periodical interest rate=0.5%
	N=periods=60
	FV=756.92*[(1+0.005)^60-1]/(0.005)
	FV=52810.33
	So they can afford a down paymnet for house for $52810.33
	Down paymnet is 15% , So cost of house=52810.33/15%=	$                     352,069
	Loan to be taken =352069-52810.33=	$                299,258.54
	Mortgae Loan monthly installment A is given by below formula
	A= [i*P*(1+i)^n]/[(1+i)^n-1]
	i=4.5%/12=0.375%
	P=299258.54
	n=360 months
	A= [0.00375*299258.54*(1+0.00375)^360]/[(1+0.00375)^360-1]
	A=1517.67
	So Monthly Mortgage payment =$1,517.67