Question

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.)

Answer 1

Miles will pay $5756.64 over four years, while Nick will pay $6360.96. Therefore, Nick will have paid $604.32 more than Miles.

Step-by-step explanation:

To calculate the total amount paid by each person, we need to determine the monthly payment for each loan and then multiply it by the number of payments over four years.

For Miles:

1. Convert the annual interest rate to a monthly rate by dividing it by 12: 7.75% ÷ 12 = 0.6458%

2. Convert the monthly interest rate to a decimal: 0.6458% ÷ 100 = 0.006458

3. Calculate the monthly payment using the formula:

Monthly Payment = Loan Amount * (Monthly Rate/(1 - (1 + Monthly Rate)^(-Number of Payments)))

Monthly Payment = $5,000 * (0.006458/(1 - (1 + 0.006458)^(-48)) = $119.93

For Nick:

1. Convert the annual interest rate to a monthly rate: 13.10% ÷ 12 = 1.0917%

2. Convert the monthly interest rate to a decimal: 1.0917% ÷ 100 = 0.010917

3. Calculate the monthly payment using the same formula:

Monthly Payment = $5,000 * (0.010917/(1 - (1 + 0.010917)^(-48)) = $132.52

Now, we can calculate the total amount paid by each person:

Amount paid by Miles: $119.93 * 48 = $5756.64

Amount paid by Nick: $132.52 * 48 = $6360.96

To find the difference between the two amounts, we subtract:

$6360.96 - $5756.64 = $604.32

Therefore, Nick will have paid $604.32 more than Miles.