I am working on a discussion question where I have to pretend I am purchasing my dream car. I have to use the price of the car minus the down payment to get my figure. Then I must decide which financing is the better value. The bank s interest rate is 2.0% for 48 months, and the finance company’s is 10% for 36 months, but they will refund 5% of the cars original price. I have already determined the monthly interest for each scenario. I have an estimate I work through basic math that I checked with an amortization calculator. My instructor wants us to use PV to determine what my monthly payment would be in both instances, and how much interest I would pay over the life of the loan. I have started the problem, but cannot finish it, I got an answer for the first scenario, the loan of 0.2% from the bank, but it does not match the answer I get from the amortization calculator. I know that I am forgetting something that is making it hard to figure these problems. If anyone could help I would be very grateful. I have tried very hard to complete this work on my own, and only need some assistance in understanding what I am doing wrong.
Discussion Question One:
Imagine that you have decided you need a new car, but not any car will do; you have decided to purchase the car of your dreams. Conduct some research as to the cost of this car. You have determined in this imagined scenario that you could afford to make a 10% down payment. You can borrow the balance either from your local bank using a four-year loan or from the dealership’s finance company. If you purchase from your dealership’s finance company, the APR will be 10% with your 10% down and monthly payments over three years. However, the dealership will give you a rebate of 5% of the car price after the three year term is complete. You want the best deal possible, so you consider the following questions:
What type of car have you selected, and what will it cost?
What is the interest rate from your local bank for a car loan for four years?
What will your payment be to your local bank, assuming your 10% down payment? Be sure to use the formula provided in Chapter 4 and show your work. How much will that car have cost in four years?
What will your payment be to the dealership finance company assuming your 10% down payment? Be sure to use the formula provided in Chapter 4 and show your work. How much will that car have cost in 3 years?
Which is the better deal and why?
My answer so far:
Now for the hard part, financing. I am expecting to pay 10% down, which on $88,045 is $8,804.50. To figure the percentage I just use this simple formula because it is easy and fast.
$88,045 x .10 = 8,804.50. This is the minimum amount I need to have available for a down payment whether I decide to acquire a bank loan or dealer financing.
An auto loan is an amortized loan, and uses simple interest, not compound interest. When you spread your payments over a longer period, you generally pay a lower monthly payment, however, you will pay more in interest over all. The text book states, “An amortized loan is a direct application of the present value of an annuity. The original amount borrowed is the present value of the annuity (PV0), while loan payments are the annuity’s cash flows (CFs)” (Hickman, 2013. P. 99).
I researched several banks. As of July 1rst, Alaska Credit Union is offering 2.25% to customers with good to excellent credit. To make it a little easier, I will change that to 2.0% for this exercise.
After applying my $8,804.50 down payment I am financing the remaining $79,241 (rounded to the nearest dollar).
My first step is to do a quick estimate using simple calculations to get a ball park figure of my financing options, which I double checked using a amortization calculator.
The Alaska loan would cost me $ 82,934 over the life of the loan, with payments of $1,728 per month for 48 months. Under this loan I will have paid about $3,694 in interest over the life of the loan.
My monthly interest rate will be 0.2/ 12 months = 0.01666%
Next I figure the numbers using the PV method
79241= 1-[1/(1.01666)^48] = 0.547556207274 79241/0.547556207274=1447.17
The dealership financing would cost $ 92,052 over the life of the loan with payments of $2,557 per month for 36 months. Under this loan I will have paid $12,807 in interest over the life of the loan.
My monthly interest will be .10 / 12 = 0.08333%
79241= 1-[1/(1.08333)^36] = 0.943945267913 79241/0.943945267913
Now, factoring in the 5% cash back from the dealer. Here I was a little confused because the discussion question says the dealer will rebate 5% of the car price after the three year term is complete. It does not stipulate if this refers to the cars price before or after the 10% down payment.
I decided to take it literally and use the original price of $88,045, before the down payment, which means 88,045 x .05 = 4405.25 is my rebate. If you subtract 4405.25 from 92,050 you are still left with $87,647 rounded to the nearest dollar. A difference of $4713, making the loan from the bank the better deal.
I am relatively sure that I am correct that the bank loan is the better option.
Can you help me finish the steps, and, or correct mistakes I am making so I can correctly complete the problems?
Also, do you have any tips as the fastest, most accurate way to calculate the bond price below?
Discussion Question 2:
Assume interest rates for bonds today is 5% for an AAA rated bond. Calculate the price of the bond you have selected relative to the 5%. Is the bond selling at a premium or a discount? Why? Be sure to show how you arrived at your answer. What other factors may influencethe value of a bond?
For this exercise I choose Costco, with a price of 100.77
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