Question

You buy a car for $40,000. You agree to a 6 year loan with a annual interest 6 percent.

a. What is your required monthly payment?

b. What is the total amount interest payment over this period?

C. Show the difference in the total interest payment if the payment was done yearly instead of monthly?

Answer 1

a) Given, total loan amount = $40,000

     Annual interest rate         = 6%

     No of years                        = 6

Thus, required monthly payment = P*r*[1+r]n/ ([(1+r]n ]- 1)

Substituting the values, we have; monthly payment = 40,000*6*[1+6]6 / [(1+6]6]-1)

Thus, we have monthly payment = $662.92

b) Total number of payments = 72

   Thus, total amount paid       = 72*662.92

                                                      = $47,730.24

Thus, total interest paid         = $7,730.24

c) Substituting for annual payment in he given equation, we have

        Required total payment = P*r*[1+r]/ ([(1+r]n ]- 1)

                                                   = $8,807

Thus, difference                      = 8,807-7730.24

                                                    = $1076.76