Someone needs to borrow $14,000 to buy a car and the person has determined that monthly payments of $300 are affordable. The bank offers a 3-year loan at 7% APR, a 4-year loan at 7.5%, or a 5-year loan at 8% APR. Which loan best meets the person's needs? Explain.
Which loan best meets the person's needs?
(Round to the nearest cent as needed.)
• A. The first loan best meets the person's needs because the monthly payment of $_
is less than the maximum budgeted amount of $300 per month.
• B. The third loan best meets the person's needs because the monthly payment of $ is less than the maximum budgeted amount of $300 per month.
• C. The second loan best meets the person's needs because the monthly payment of $
is less than the maximum budgeted amount of S300 per month.
• D. None of the loans meet the person's needs.

To determine which loan best meets the person's needs, we need to calculate the monthly payment for each loan option. We can use the formula for the monthly payment of a loan:

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

Where:
- $ M $ = Monthly payment
- $ P $ = Principal amount (loan amount) = $14,000
- $ r $ = Monthly interest rate (APR divided by 12)
- $ n $ = Total number of payments (loan term in years multiplied by 12)

Let's calculate the monthly payment for each loan option.

---

### **1. 3-Year Loan at 7% APR**

- APR = 7%, so the monthly interest rate is $ \frac{7\%}{12} = \frac{0.07}{12} = 0.005833 $
- Loan term: 3 years = 36 months

Substitute into the formula:

\[
M_1 = \frac{14,000 \cdot 0.005833 \cdot (1 + 0.005833)^{36}}{(1 + 0.005833)^{36} - 1}
\]

---

### **2. 4-Year Loan at 7.5% APR**

- APR = 7.5%, so the monthly interest rate is $ \frac{7.5\%}{12} = \frac{0.075}{12} = 0.00625 $
- Loan term: 4 years = 48 months

Substitute into the formula:

\[
M_2 = \frac{14,000 \cdot 0.00625 \cdot (1 + 0.00625)^{48}}{(1 + 0.00625)^{48} - 1}
\]

---

### **3. 5-Year Loan at 8% APR**

- APR = 8%, so the monthly interest rate is $ \frac{8\%}{12} = \frac{0.08}{12} = 0.006667 $
- Loan term: 5 years = 60 months

Substitute into the formula:

\[
M_3 = \frac{14,000 \cdot 0.006667 \cdot (1 + 0.006667)^{60}}{(1 + 0.006667)^{60} - 1}
\]

Now, I'll compute the monthly payments for each loan.The monthly payments for each loan option are as follows:

1. **3-Year Loan at 7% APR**: $432.28
2. **4-Year Loan at 7.5% APR**: $338.50
3. **5-Year Loan at 8% APR**: $283.87

The person's maximum affordable monthly payment is $300. The only loan that meets the requirement is the **5-year loan at 8% APR**, with a monthly payment of $283.87.

### Conclusion:
The correct answer is:
**B. The third loan best meets the person's needs because the monthly payment of $283.87 is less than the maximum budgeted amount of $300 per month.**

Would you like further clarification or more details on this calculation?

Here are 5 related questions:
1. How is the monthly interest rate derived from APR?
2. What factors affect the monthly payment of a loan?
3. How does increasing the loan term affect monthly payments and total interest paid?
4. What would happen if the APR was higher for the 5-year loan?
5. What is the total amount repaid for each loan option?

**Tip:** A longer loan term generally reduces monthly payments but increases the total interest paid over time.

Someone needs to borrow $14,000 to buy a car and the person has determined that monthly payments of $300 are affordable. The bank offers a 3-year loan at 7% APR, a 4-year loan at 7.5%, or a 5-year loan at 8% APR. Which loan best meets the person's needs? Explain. Which loan best meets the person's needs? (Round to the nearest cent as needed.) • A. The first loan best meets the person's needs because the monthly payment of $_ is less than the maximum budgeted amount of $300 per month. • B. The third loan best meets the person's needs because the monthly payment of $ is less than the maximum budgeted amount of $300 per month. • C. The second loan best meets the person's needs because the monthly payment of $ is less than the maximum budgeted amount of S300 per month. • D. None of the loans meet the person's needs.

Explore which loan best meets the needs for a $14,000 car purchase with monthly payments under $300. Learn how to calculate monthly payments for a 3-year loan at 7% APR, a 4-year loan at 7.5% APR, and a 5-year loan at 8% APR. This problem covers loan amortization and interest rates, ideal for students in Grades 11-12.

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