Question

Suppose Capital One is advertising a 60​-month, 5.06 % APR motorcycle loan. If you need to borrow $ 8 comma 400 to purchase your dream​ Harley-Davidson, what will be your monthly​ payment?​ (Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

The student's question is about calculating the monthly payment for a $8,400 motorcycle loan with a 5.06% APR over 60 months. By using the formula for an amortizing loan, which includes the principal, monthly interest rate, and the number of payments, the monthly payment amount can be determined.

Step-by-step explanation:

The question refers to calculating a monthly payment for a motorcycle loan. Given the details of the loan, which include an amount of $8,400 with an APR of 5.06% over a time period of 60 months, we can calculate the monthly payment using the formula for an amortizing loan. The formula incorporates the principal amount, the monthly interest rate, and the number of monthly payments and typically takes the form of:

P = [r*PV] / [1 - (1 + r)^-n]

Where P is the monthly payment, PV is the present value of the loan (initial amount borrowed), r is the monthly interest rate (APR divided by 12), and n is the number of payments (terms in months).

To find the monthly interest rate, we divide the APR by 12. So, 5.06% APR divided by 12 months gives us a monthly interest rate of 0.421667%. Then we plug into the formula along with the principal amount of $8,400 and 60 months to get the monthly payment.

Answer 2

The monthly payment n the motorcycle will be for 158.75 dollars

Step-by-step explanation:

We need to solve for the PMT of an ordinary annuity:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 8,400 (loan)

time 60 months

rate 0.004216667 (5.06% annual divide into 12 months)

`8400 / (1-(1+0.00421666666666667)^(-60) )/(0.00421666666666667) = C\\`

C $ 158.749