Question

Capital One is advertising a​ 5 year, 5% EAR motorcycle loan. If you need to borrow $15,000 to purchase your dream Harley​ Davidson, what will your monthly payment​ be? Interest compounds monthly. Round your answer to the nearest $0.01

Answer 1

We have provisded effective annual rate, so, we willfind the monthly interest rate

Effective annual rate = [(1+Interest rate per period)^Number of periods] -1

5% = (1+i)^12 -1

0.05+1 = (1+i)^12

1.05^(1/12) = (1+i)

1.00407412378 = (1+i)

i = 1.00407412378 -1

i = 0.40741237836%

Monthly payment = P * R*(1+R)^N / [(1+R)^N -1]

= 15000 *  0.40741237836% * (1+ 0.40741237836%)^60 / [(1+0.40741237836%)^60 -1]

= 61.111856754 *1.2762815625 / (1.2762815625-1)

= 77.9959360253 / 0.2762815625

Monthly payment = $282.31