Question

(MSRP) Model: 2016 Ferrari 488 Spider

Price :$276,450

Part III: $$ Your Financing Options $$

In this section, you will have to go online to determine the interest rate incurred when you finance a car.

Let’s say you are unable to put a down payment on a car and you had to finance the full amount. Take the MSRP of your car from part 1).

Go to https://calculator.me/vehicle/

Type the Vehicle price (which total the loan amount), the interest rate and the loan terms (number of years). Set other values to zero.

(12 points) Use the Calculator to determine your monthly payment if you were to get 10% interest by filling the table below. the loan was 60 months (5years), 48 months (4 years), 36 months (3 years), 24 months (2 years) and 12 months ( 1 year).

Loan Term/ monthly payment	Monthly payment (for 10% interest rate)	Total interest paid after the term of the loan for 10% interest	Monthly payment for 6% interest rate	Total interest paid after the term of the loan for 6% interest
60 months/$5,036.00
48 months/$6,174.24
36 months/$8,073.33
24 months/$11,874.54
12 months/$23,284.24

(3 points) How does the monthly payment change as a function of the loan term?

(3 points) How does the total interest paid change as a function of the loan term?

(3 points) Does it pay off to have a lower interest rate? Why, Give an example using numbers from the table and calculate the actual savings in interest for a loan term of your choice.

Part IV: Modeling Using Excel

Suppose you decide to buy a new car for $ 30000. Suppose that you have no money for a down payment and that you decide to finance the whole amount. The dealer offers several financing option through a local bank. He offers you the option of financing the car over 12 months, 24 month, 36 months, 48 months and 60 months.

Unfortunately, the interest rate was pretty high and equal to 10%. The table below shows the total interest paid after the term of loan if you were to finance it.

Total Interest Paid after the term of the loan	0	$ 1649.72	$3224.35	$4848.56	$6522.12	8244.68
Term of the loan	0	12 months	24 months	36 months	48 months	60 Months

(a) (3 points) Graph the total interest paid as a function of the term of the loan in Excel.

(b) (3 points) Find the linear function that best fits the total interest paid as a function of the term of the loan.

(c) (3 points)FROM THIS FUNCTION, calculate how much you have paid in interest 30 month after you had purchased the car assuming you financed it?

Part V: Reflection

(10 points) Your friend John is planning to finance a car. He is unsure about his budget, but thinks he can afford a $15, 000 car. He has only $2,000 to put down and he earns about $1500 a month after taxes. John contacts you for advice. What advice would you give him? (Please write a 200 to 300-word letter to John, advising him on how much he should spend on a car, what interest rate he should try to get and how much he can afford in monthly payments). REFER TO THE TABLE AND CLASS DISCUSSIONS and to the rubric below.

Make sure you answer the following in your paragraph:

Make sure you write a coherent paragraph.

Mention the amount John needs to finance.

Decide how much John can afford a month to pay towards his car monthly payment.

Give John several examples: choose two different interest rates and for each interest rate you choose give the monthly payment for two different loan terms ( 3 years versus 5 years etc..). Don’t forget to use the calculator we used in class.

Bare in mind what you learned from the tables in your conclusion, for e.g. the longer the loan term the more interest you’ll end up paying the bank.

More importantly consider John to be your real friend and do not hesitate in elaborating your response and express your opinion!

Reading: How to Finance a Car and Get a Car Loan

http://usnews.rankingsandreviews.com/cars-trucks/How-to-Finance-a-Car/(accessed March 18 2012) By Jamie Page Deaton

Let's be honest: most people aren't thinking about buying a new car now. The Great Recession has put new cars out of most people's minds. But, if you really need a new car, you can get some great discounts and incentives. With the credit market still tight, the problem most people have is getting the financing to take advantage of the deals available.

Car financing is tricky even when the credit market is good. Now that the credit market is tight, it's back to basics for buyers and lenders. Check out the car financing basics covered below to make sure you get the best car loan for your next vehicle.

The Basics of Car Loans

Getting a car loan simply means borrowing money to pay for it. Borrowing money probably isn't new to you -- everyone's bummed $10 from friends. When you borrow from a lender, the amount you borrow is called the loan principle. Though the basic idea behind borrowing money for a car is the same, when it comes time to pay the loan back, things get a little complicated.

Unless your friends don't like you much, they're not going to charge you interest on money you borrow. But professional lenders will. A bank isn't your friend and doesn't lend money out of the goodness of its heart. It needs a financial incentive. That's what interest provides for the lender: a financial incentive to lend money.

When you take out a loan for a car, it'll come with an interest rate -- a certain percentage of a loan that you must pay back in addition to the original loan amount. So, if you borrow $20,000 for a car at a 5 percent interest rate, you're going to end up paying the bank $21,000 over the life of the loan -- that's the principle, plus the interest.

The Car Loan Term

The life of the loan, or loan term, simply refers to the amount of time you have to pay the lender back. If you sign up for a five-year term, in five years you'll pay the money back and will own the car free and clear. What the loan term doesn't mean is that five years from now you'll have to come up with all of the money. The vast majority of auto loans are repaid in monthly installments. You send the lender a set amount each month and slowly pay off the loan.

Most people think that when you finance a car, the finance company lends you the money and the car is yours. That's a simple way of looking at it. In reality, however, the lender is buying the car and letting you use it. The lender technically owns the car, though you agree to be responsible for it. In fact, you won't have the title to the car until you make your last loan payment. Miss loan payments and the lender repossess the car. Each payment you make buys you a little more of the car, but you don't fully own it until the loan is paid off.

Now that you know the basics, you're probably wondering how people can screw up financing a car. Believe it or not, there are plenty of ways.

Your Credit Score

All interest rates are not created equal. Some people get charged more interest, and some get charged less. Obviously, you want to get charged less. The interest rate lenders charge is based largely on your credit score -- a number that's assigned to you based on how much other debt you have and how good you've been about paying bills on time. Lenders use the score to assess how likely you are to pay them back. If your score is low, they'll think you're not likely to repay the auto loan and charge you more money to cover that risk.

Young people often have lower credit scores than older people, even if they've been good about staying out of debt and paying their bills. That's because young people don't have long credit histories, which makes it difficult for lenders to tell how much of a risk they are. As a result, people without long credit histories can be charged higher interest rates too.

You should know what your credit score is and do your best to make sure it's high. For a small fee, you can get it through Equifax, Experian or TransUnion. If your score is not as high as you'd like, paying off old bills (like credit card debt) and paying all bills on time (the full balance, not just the minimum due) for six to nine months should bring your score up and interest rate down.

Apply, Apply, Apply

You wouldn't just apply to one job or one college, so you shouldn't apply to just one lender for a car loan. Contact your bank, local credit unions and other lenders to find out what they're offering. You'll have to fill out loan applications, which will ask for your employment history, income, expenses and debts. Do not be tempted to exaggerate your income or misstate your expenses. Everything you fill out on a loan application will be verified and lying will get you into serious trouble. The lender will pull your credit history and credit score and make you a loan offer based on that information.

Take some time to go over all the offers. Don't just look at the interest rates -- avoid offers that charge you a lot of fees. Also, watch out for loans that have a prepayment penalty; that's a charge that you'll owe if you pay the loan off early. Paying the loan off early may not be something you'll be able to do, but if your long-lost Aunt Maybel dies and leaves you a fortune, paying it off could save you a lot of money -- and you don't want to pay extra to do it.

Answer 1

Calculation of monthly payment & Interest at various rates of interest.

Loan Term/ monthly payment	Monthly payment (for 10% interest rate)	Total interest paid after the term of the loan for 10% interest	Monthly payment for 6% interest rate	Total interest paid after the term of the loan for 6% interest
60 months/$5,036.00	276,450 / 47.54 = 5,815	5815 x 60 – 276,450 = 72,450	5,324	42,990
48 months/$6,174.24	276,450 / 39.75 = 6,955	57,390	6,471	34,158
36 months/$8,073.33	276,450 / 31.18 = 8866	42,726	8,390	25,590
24 months/$11,874.54	276,450 / 21.76 = 12,705	28,470	12,232	17,118
12 months/$23,284.24	276,450 / 11.40 = 24,250	14,550	23,770	8,790

NOTE: Calculation of Cumulative present value at 10% interest.

Convert yearly interest rate to monthly.

(1+ interest rate) = (1 + (interest / 12) )¹²

1.10^1/12 = (1 + interest /12)

1.00797414 = (1+interest /12)

(1.00797414 – 1) x 12 = interest rate

0.09569 = interest rate (convertible monthly)

NOW we can calculate the cumulative present value with the function

Cumulative present value = 12 x {1 – (1.10)^-n} / 0.09569

Where n is the term of the loan.

5 year loan = 47.54

4 year loan = 39.75

3 year loan = 31.18

2 year loan = 21.76

1 year loan = 11.40

Similarly for 6% interest,

5 year loan = 51.93

4 year loan = 42.72

3 year loan = 32.95

2 year loan = 22.60

1 year loan = 11.63

Dear Student, this is the formula taught in acturies course. It's a shorter way to compute the cumulative present value at particular interest rate. Please ask the questions where you dont understand.