You want to purchase a new car. The price of the car is ...

You want to purchase a new car. The price of the car is $\$ 24,035 .$ The dealer is currently offering a special promotion: (1) You can choose a $\$ 1500$ rebate up front and finance the balance at $6 \%$ for 60 months, or (2) $0 \%$ financing for the first 36 months and $6 \%$ financing for the remaining 24 months of your loan. Which is the better deal? Justify your answer by computing your monthly payments over 60 months under each of the two options.

Key Concepts

Loan Amortization

Loan amortization is the process of spreading out a loan into a series of fixed payments over time. Each payment contributes to both the interest due and the reduction of the principal balance. Understanding loan amortization is essential when evaluating how different financing options impact the structure of payments over the life of a loan.

Annuity Payment Formula

The annuity payment formula is used to calculate equal periodic payments on a loan or investment, given a fixed interest rate and a set number of periods. This formula combines the concepts of present value and compound interest, allowing one to determine the payment amount that fully amortizes the loan over its term.

Interest Rate Conversion

Interest rate conversion involves translating an annual interest rate into a rate applicable to the payment period, such as a monthly rate. This is crucial because many financial calculations, including loan amortization, require the interest rate to match the payment period to ensure accurate computation of payments and interest accumulation.

Comparing Financing Options

Comparing financing options involves analyzing different loan structures to determine which one is more cost-effective over the duration of the loan. This process often includes calculating the monthly payments, total interest paid, and understanding how varying interest rates at different phases of the loan term affect the overall cost.

Transcript

00:01 All right, everybody, here on this problem, we've got another loan problem.

00:03 Now, it's not quite as complicated as it looks.

00:05 All right, so let's go ahead and run through this.

00:07 They're giving you two options here.

00:10 Option number one is zero percent interest, 48 months, and then the car costs $18 ,000.

00:18 Option two is still 48 months, 7 .98 % interest.

00:22 Now, the car still costs $18 ,000, but they give you a $2 ,000 discount if you take this option.

00:27 So it means the car is really only going to cost $6 .9%.

00:30 $16 ,000 over here.

00:32 Now, you want to use this formula that they give you to determine which of these two options is going to be the cheapest for you.

00:38 All right.

00:39 Now, let's just think about option number one over here for a second.

00:42 Forget the other parts.

00:43 Let's just look at option number one.

00:45 Now, it's a zero percent interest.

00:48 So it means your monthly payment, your monthly payment is just going to be how much it costs you total, divided by how many total payments you have.

01:00 So 18 ,000 divided by 48.

01:03 You don't need to use that complicated formula for this part, because there's no actual interest involved.

01:09 It's just how much the car cost divided by how many different payments you're going to make on it.

01:14 And so when you do that, that gives us $375.

01:19 So the monthly payment for that option is going to be $375.

01:23 So now let's consider option number two here.

01:28 Let's come back up here and let's look at option number two.

01:31 Now, because option number two has actual interest involved, a 7 .98 % interest, that tells you you're going to have to use that formula here.

01:41 So it tells you it's 48 months.

01:44 N is the number of months you have.

01:46 So it means n is equal to 48.

01:49 So in this formula, everywhere that there's an n, let's come back up here and replace both of those ends with a 48.

01:59 Come back up here, replace both of those ends with a 48.

02:03 It's 7 .98 % interest.

02:05 That tells you what your r is.

02:07 So r is 0 .0798.

02:12 Okay, 0 .0798.

02:15 You'd have to have your interest as a decimal.

02:18 And so that's what we need to come back up here and replace all of our r's with...

Please give Ace some feedback