Question

QUESTION 10 Car payments are determined using simple interest. If you don’t remember this formula, go back and look it up! To finance your vehicle purchase you have two choices. Write two equations, one for each bank, that models the banks' loan options using x for the price of the vehicle and y to represent the total cost (price, interest and origination fees) paid on each loan. Be sure to label which equation goes with which bank. Bank A: Finance the full price of the vehicle at 5% with an origination fee of $300 paid over 5 years. Bank B: Finance the full price of the vehicle at 3.5% paid over 6 years (no additional fees). car costs:$31,690.

QUESTION 12 Use the equations you came up with for bank financing options to calculate the following: Total cost of your vehicle using bank A Monthly payment of your vehicle using bank A Total cost of your vehicle using bank B Monthly payment of your vehicle using bank B Show all of your work using the equation editor and label each solution.

QUESTION 13 Taking into account your allowed car payment range and the payments you determined for Bank A and Bank B, can you afford to purchase your vehicle? Express your answer in paragraph form. If you cannot afford the vehicle, explain why based on your budget values you determined. If you will purchase the vehicle, which bank will you finance your vehicle through and why?

Answer 1

QUESTION 10)

Simple interest = P x T x R

where ,

P = principal amount (in this case cost of the car)

T = time period

R = interest rate per annum

BANK A:

x = price of the vehicle

y = total cost

so

y = x + 5 * 0.05 * x + 300

here x = car price ,

interest = 5% = 0.05

time = 5 years

so total interest for 5 years = 5 * 0.05 * x

origination fee = $300

since y includes all three we add all of them

BANK B:

y = x + 6 * 0.035 * x

here interest rate = 3.5% = 0.035

time = 6 years

total interest for 6 years = 6 * 0.035 * x

in this bank there are no additional costs involved

QUESTION 12)

BANK A

Total cost (y) = x + 5 * 0.05 * x + 300

given car price = $31,690

so y = 31690 + 5 * 0.05 *31690 + 300

y = 31690 + 7922.5 + 300

y = $39,912.5

monthly payments = 39912.5 / 60 = $665.21

t = 5 years = 60 months

BANK B

y = x + 6 * 0.035 * x

y = 31690 + 6 * 0.035 *31690

y = 31690 + 6654.9

y = $38344.9

monthly payments = 38,344.9 / 72 = $532.57

t = 6 years = 72 months

QUESTION 13)

If we want to purchase the car it is better to finance from BANK B as it results in lower cash outflow even though time period is one year more than BANK A

( answer the remaining part based on your income,budgeted expenses and savings)