Questions: Miles and Nick each separately apply for and receive loans worth 5,000 apiece. Miles has a very good credit score, so his loan has an APR of 7.75%, compounded monthly. Nick's credit score is rather low, so his loan has an APR of 13.10% interest, compounded monthly. If both of them repay their loans over a four year period, making equal monthly payments based on their own loan, how much more will Nick have paid than Miles? (Round all dollar values to the nearest cent.) a. 619.68 b. 267.50 c. 1,609.57 d. 1,070.00 Please select the best answer from the choices provided

Solution Steps

To find the monthly payments for both Miles and Nick, we use the formula for the monthly payment on an amortizing loan:

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

For Miles:

• \( P = 5000 \)
• \( r = \frac{0.0775}{12} = 0.0064583333 \)
• \( n = 4 \times 12 = 48 \)

Calculating Miles' monthly payment: \[ M_{\text{Miles}} = \frac{5000 \times 0.0064583333 \times (1 + 0.0064583333)^{48}}{(1 + 0.0064583333)^{48} - 1} \approx 121.4787 \]

For Nick:

• \( P = 5000 \)
• \( r = \frac{0.1310}{12} = 0.0109166667 \)

Calculating Nick's monthly payment: \[ M_{\text{Nick}} = \frac{5000 \times 0.0109166667 \times (1 + 0.0109166667)^{48}}{(1 + 0.0109166667)^{48} - 1} \approx 134.3858 \]

Next, we calculate the total payments made by both Miles and Nick over the four-year period.

For Miles: \[ \text{Total}_{\text{Miles}} = M_{\text{Miles}} \times n = 121.4787 \times 48 \approx 5830.9781 \]

For Nick: \[ \text{Total}_{\text{Nick}} = M_{\text{Nick}} \times n = 134.3858 \times 48 \approx 6450.5172 \]

Now, we find the difference in total payments between Nick and Miles: \[ \text{Difference} = \text{Total}_{\text{Nick}} - \text{Total}_{\text{Miles}} \approx 6450.5172 - 5830.9781 \approx 619.5391 \]

Final Answer