Someone needs to borrow ​$12 comma 000 to buy a car and the person has determined that monthly payments of ​$250 are affordable. The bank offers a 3​-year loan at 6​% ​APR, a 4​-year loan at 6.5​%, or a 5​-year loan at 7​% APR. Which loan best meets the​ person's needs? Explain.
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Part 1
Which loan best meets the​ person's needs?
​(Round to the nearest cent as​ needed.)
A.
The first loan best meets the​ person's needs because the monthly payment of ​$
  
enter your response here is less than the maximum budgeted amount of ​$250 per month.
B.
The third loan best meets the​ person's needs because the monthly payment of ​$
  
enter your response here is less than the maximum budgeted amount of ​$250 per month.
C.
The second loan best meets the​ person's needs because the monthly payment of ​$
  
enter your response here is less than the maximum budgeted amount of ​$250 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 using the loan payment formula for an installment loan:

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

Where:
- $ P $ is the monthly payment
- $ r $ is the monthly interest rate (annual rate divided by 12)
- $ PV $ is the principal amount (the loan amount)
- $ n $ is the total number of payments (loan term in years multiplied by 12)

Given:
- Loan amount ($ PV $) = $12,000
- Affordable monthly payment = $250

Let's calculate the monthly payments for each loan option:

1. **3-year loan at 6% APR**:
   - Annual interest rate = 6%
   - Monthly interest rate ($ r $) = $ \frac{6\%}{12} = 0.5\% = 0.005 $
   - Total payments ($ n $) = 3 years * 12 = 36 months

2. **4-year loan at 6.5% APR**:
   - Annual interest rate = 6.5%
   - Monthly interest rate ($ r $) = $ \frac{6.5\%}{12} \approx 0.5417\% = 0.005417 $
   - Total payments ($ n $) = 4 years * 12 = 48 months

3. **5-year loan at 7% APR**:
   - Annual interest rate = 7%
   - Monthly interest rate ($ r $) = $ \frac{7\%}{12} \approx 0.5833\% = 0.005833 $
   - Total payments ($ n $) = 5 years * 12 = 60 months

Let's calculate the monthly payments for each of these loans.The monthly payments for each loan option are as follows:

1. **3-year loan at 6% APR**: $365.06
2. **4-year loan at 6.5% APR**: $284.58
3. **5-year loan at 7% APR**: $237.61

Since the person can afford a maximum monthly payment of $250, only the **5-year loan at 7% APR** meets their budget. Therefore, option B is the correct choice:

**B. The third loan best meets the person's needs because the monthly payment of $237.61 is less than the maximum budgeted amount of $250 per month.**

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How much interest will the person pay over the life of each loan?
2. What is the total cost of the car including interest for each loan option?
3. How much would the monthly payment be if the person could afford a slightly higher amount?
4. What is the impact of making additional payments on the 5-year loan?
5. How does the loan term affect the total amount of interest paid?

**Tip:** Always compare the total interest paid for different loan options to understand the long-term cost of borrowing.

Someone needs to borrow $12,000 to buy a car and the person has determined that monthly payments of $250 are affordable. The bank offers a 3-year loan at 6% APR, a 4-year loan at 6.5%, or a 5-year loan at 7% APR. Which loan best meets the person's needs? Explain.

Determine which loan option best meets the person's budget of $250 per month. We compare a 3-year loan at 6% APR, a 4-year loan at 6.5% APR, and a 5-year loan at 7% APR. Learn how to calculate monthly payments and select the most affordable option.

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