Please help, past due already

Question

A college student is trying to decide whether to buy or lease a motorcycle for getting to and from school. The cost of the motorcycle is $13,000, including tax. a. Determine the monthly payment on a loan for the bike with a financing term of 36 months, an APR of 5.9%, compounded monthly. b. Determine the monthly payment on a lease for 24 months, an APR of 4.1%, compounded monthly. The deprecation is 15% per year. c. Based solely on the monthly payment, which option is the most affordable for this student

Answer 1

a. To calculate the monthly payment on a loan for the motorcycle, we can use the following formula:

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

where P is the monthly payment, r is the monthly interest rate, PV is the present value of the loan (the cost of the motorcycle), and n is the number of payments (the financing term).

In this case, we have:

PV = $13,000 n = 36 months APR = 5.9%

To find the monthly interest rate, we first need to convert the APR to a monthly rate:

r = (1 + APR/12)^12 - 1 = 0.004867

Substituting these values into the formula, we get:

P = (0.004867 * $13,000) / (1 - (1 + 0.004867)^-36) = $392.68

Therefore, the monthly payment on the loan would be $392.68.

b. To calculate the monthly payment on a lease, we need to determine the monthly depreciation rate, which is 15% / 12 = 0.0125. We can then use the following formula:

P = (RV + (RV - PV) * r) / n

where P is the monthly payment, RV is the residual value of the motorcycle (the value of the motorcycle at the end of the lease), PV is the present value of the lease (the cost of the motorcycle), r is the monthly interest rate, and n is the number of payments (the financing term).

In this case, we have:

PV = $13,000 n = 24 months APR = 4.1% depreciation rate = 0.0125

To find the monthly interest rate, we first need to convert the APR to a monthly rate:

r = (1 + APR/12)^12 - 1 = 0.003369

To find the residual value of the motorcycle, we can use the formula:

RV = PV * (1 - depreciation rate)^n

RV = $13,000 * (1 - 0.0125)^24 = $8,448.81

Substituting these values into the formula, we get:

P = ($8,448.81 + ($8,448.81 - $13,000) * 0.003369) / 24 = $262.41

Therefore, the monthly payment on the lease would be $262.41.

c. Based solely on the monthly payment, the lease option appears to be the most affordable for the student, as the monthly payment is lower than the loan payment. However, it's important to consider other factors, such as the length of time the student plans to use the motorcycle, their driving habits, and any mileage restrictions or penalties that may apply under the lease agreement.