To determine the monthly payments and the total payments for Taneesha's car financing options, we can use the standard formula for loan amortization:

$M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}$ Where:

• $M$ = Monthly payment
• $P$ = Loan principal (the amount borrowed)
• $r$ = Monthly interest rate (annual interest rate divided by 12)
• $n$ = Total number of payments (loan term in months)

First Option: 3 years at 9% interest rate

• Principal $P = 13,000$
• Annual interest rate = 9% → Monthly interest rate $r = \frac{9\%}{12} = 0.0075$
• Loan term = 3 years → $n = 3 \times 12 = 36$ months

1. Monthly payment for the first option:

$M = \frac{13000 \times 0.0075 \times (1 + 0.0075)^{36}}{(1 + 0.0075)^{36} - 1}$

Solving this:

$M \approx 413.57$

So, the monthly payment for the first option is $413.57.

2. Total payments for the first option: To find the total payments, multiply the monthly payment by the number of months:

$\text{Total} = 413.57 \times 36 = 14,888.52$

So, the total payments for the first option are $14,888.52.

Second Option: 6 years at 7% interest rate

• Principal $P = 13,000$
• Annual interest rate = 7% → Monthly interest rate $r = \frac{7\%}{12} = 0.0058333$
• Loan term = 6 years → $n = 6 \times 12 = 72$ months

3. Monthly payment for the second option:

$M = \frac{13000 \times 0.0058333 \times (1 + 0.0058333)^{72}}{(1 + 0.0058333)^{72} - 1}$

Solving this:

$M \approx 223.43$

So, the monthly payment for the second option is $223.43.

4. Total payments for the second option: Multiply the monthly payment by the number of months:

$\text{Total} = 223.43 \times 72 = 16,071.04$

So, the total payments for the second option are $16,071.04.

Summary:

1. Monthly payment for the first option: $413.57
2. Total of the payments for the first option: $14,888.52
3. Monthly payment for the second option: $223.43
4. Total of the payments for the second option: $16,071.04

Do you have any questions or want more details?

Here are 5 relative questions for you:

1. What is the total interest paid in the first option?
2. How much more does Taneesha pay in total for the second option compared to the first?
3. How would the monthly payments change if the interest rate were reduced by 1% in both cases?
4. What would be the monthly payment if she chose a 4-year term at 8% interest?
5. How does the total interest paid compare between the two options?

Tip: A shorter loan term typically means higher monthly payments but less total interest paid.