Leslie has been offered the choice of either a $1,000 rebate or a 5.5 percent, 48-month loan for the new car she is purchasing. If Leslie will be financing $15,000 and she can get a 7.5 percent, 48-month loan at her credit union, should she take the $1,000 rebate or the 5.5 percent loan? (Show all work.)

15,000 * 0.075 * 4 = $4,500

4,500 - 1,000 = $3,500

15,000 * 0.055 * 4 = $3,300

Well, Leslie certainly has some options here! Let's break it down:

Option 1: $1,000 rebate
Option 2: 5.5% loan for 48 months

First, let's calculate the interest amount on the credit union loan:

Interest amount = Principal amount * Interest rate
Interest amount = $15,000 * 0.075
Interest amount = $1,125

Now, let's consider the "effective cost" of the 5.5% loan option:

Effective cost = Principal amount + Interest amount
Effective cost = $15,000 + $1,125
Effective cost = $16,125

If Leslie takes the $1,000 rebate, the effective cost of the loan would be:

Effective cost = Principal amount + Interest amount - Rebate amount
Effective cost = $15,000 + $1,125 - $1,000
Effective cost = $15,125

Comparing the effective costs:
-$16,125 for the 5.5% loan option
-$15,125 for the $1,000 rebate option

So, Leslie should go with the $1,000 rebate because it results in a lower effective cost compared to the 5.5% loan. Plus, she gets some immediate money in her pocket, and who doesn't like that?

Hope this helps, and best of luck to Leslie with her car purchase!

To determine whether Leslie should take the $1,000 rebate or the 5.5 percent loan, we need to compare the overall cost of each option.

Option 1: $1,000 rebate
Option 2: 5.5 percent, 48-month loan

Step 1: Calculate the cost of Option 1 (rebate):
The cost of Option 1 is the principal amount ($15,000) minus the rebate amount ($1,000).
Cost of Option 1 = $15,000 - $1,000 = $14,000

Step 2: Calculate the cost of Option 2 (loan):
To calculate the cost of Option 2, we will use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:
FV = Future Value (total cost of the loan)
P = Principal amount ($15,000)
r = Interest rate per period (5.5% per year, so 5.5% / 12 months = 0.4583% per month)
n = Number of periods (48 months)

Cost of Option 2 = Principal amount + Future Value
Cost of Option 2 = $15,000 + FV

Now, let's calculate the future value (FV) using the above formula:

FV = $15,000 * ((1 + 0.4583%)^48 - 1) / 0.4583%
FV = $15,000 * ((1 + 0.004583)^48 - 1) / 0.004583
FV ≈ $16,079.35

Cost of Option 2 ≈ $15,000 + $16,079.35
Cost of Option 2 ≈ $31,079.35

Step 3: Compare the costs:
Comparing the costs of Option 1 and Option 2, we can see that:

Cost of Option 1 = $14,000
Cost of Option 2 = $31,079.35

Since the cost of Option 2 is significantly higher than the cost of Option 1, Leslie should choose the $1,000 rebate as it will save her money compared to the 5.5 percent loan.

To determine whether Leslie should take the $1,000 rebate or the 5.5 percent loan, we need to compare the costs of both options over the 48-month period.

Let's calculate the cost of the 5.5 percent loan first:
1. Calculate the monthly interest rate by dividing the annual interest rate by 12: 5.5% / 12 = 0.0045833.
2. Calculate the monthly payment using the following loan payment formula: P = (r * PV) / (1 - (1 + r)^(-n)), where P is the monthly payment, r is the monthly interest rate, PV is the present value (loan amount), and n is the number of months. In this case, P = ?, r = 0.0045833, PV = $15,000, and n = 48.
P = (0.0045833 * 15000) / (1 - (1 + 0.0045833)^(-48))
P ≈ $359.11.
3. Calculate the total cost of the loan by multiplying the monthly payment by the number of months: $359.11 * 48 = $17,252.88.

Now, let's calculate the cost of taking the $1,000 rebate:
1. Calculate the interest on the loan amount using the following formula: Interest = r * PV, where r is the interest rate and PV is the present value (loan amount). In this case, Interest = 0.075 * $15,000 = $1,125.
2. Calculate the total cost of the loan by adding the interest to the loan amount minus the rebate:
Total Cost = PV + Interest - Rebate
= $15,000 + $1,125 - $1,000
= $15,125.

Comparing the costs:
1. Cost of the 5.5 percent loan: $17,252.88.
2. Cost of taking the $1,000 rebate: $15,125.

Since the cost of the 5.5 percent loan is higher than the cost of taking the $1,000 rebate, Leslie should choose the $1,000 rebate.