To calculate the monthly payment for the vehicle, we will use the formula for the monthly payment of an installment loan, which is given by:

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

Where:

• $M$ is the monthly payment,
• $P$ is the principal (loan amount),
• $r$ is the monthly interest rate (annual interest rate divided by 12),
• $n$ is the number of months (loan term in years multiplied by 12).

The total amount spent will be the monthly payment multiplied by the number of months.

Let's calculate the monthly payments and total amounts for each term (5 years, 4 years, and 3 years).

1. Five-Year Loan

• Principal: $P = 17,300$
• Annual Interest Rate: 8.50% → Monthly Interest Rate: $r = \frac{0.085}{12} = 0.0070833$
• Term: 5 years → $n = 5 \times 12 = 60$

$M_5 = \frac{17,300 \cdot 0.0070833 \cdot (1 + 0.0070833)^{60}}{(1 + 0.0070833)^{60} - 1}$ Now, we calculate:

2. Four-Year Loan

• Principal: $P = 17,300$
• Annual Interest Rate: 8.50% → Monthly Interest Rate: $r = 0.0070833$
• Term: 4 years → $n = 4 \times 12 = 48$

$M_4 = \frac{17,300 \cdot 0.0070833 \cdot (1 + 0.0070833)^{48}}{(1 + 0.0070833)^{48} - 1}$ Now, we calculate:

3. Three-Year Loan

• Principal: $P = 17,300$
• Annual Interest Rate: 8.50% → Monthly Interest Rate: $r = 0.0070833$
• Term: 3 years → $n = 3 \times 12 = 36$

$M_3 = \frac{17,300 \cdot 0.0070833 \cdot (1 + 0.0070833)^{36}}{(1 + 0.0070833)^{36} - 1}$ Now, we calculate:

Let me compute these values for you.Here are the results:

1. Five-Year Loan (60 months)

• Monthly Payment: $354.94
• Total Amount Spent: $21,296.16

2. Four-Year Loan (48 months)

• Monthly Payment: $426.42
• Total Amount Spent: $20,467.95

3. Three-Year Loan (36 months)

• Monthly Payment: $546.12
• Total Amount Spent: $19,660.26

Observations:

• As the loan term shortens, the monthly payment increases.
• However, the total amount spent decreases with shorter loan terms, since you pay less interest over time.

Would you like to explore any of these results further?

Here are 5 relative questions:

1. How much interest is paid in each scenario?
2. What happens to the total interest paid if the interest rate increases?
3. How would a down payment affect the monthly payment?
4. How does the loan duration impact the total amount paid?
5. What is the effect of making extra payments on the loan?

Tip: Shorter loan terms save you more money in the long run, even if the monthly payments are higher.