Question

5. You bought a used car for $4,000.00 at a nominal interest rate of 6%. You agreed to pay for the car in 12 equal monthly payments, beginning with the first payment at the time of the purchase of the car. a) What is the monthly payment? b) Immediately after making the fifth payment, you made an arrangement with the company to pay back the rest of the loan with one single payment at the time when the sixth payment was due. What is your sixth payment?

Answer 1

Answer (a) : The Total price of the used Car = $4000

                       If the agreement is to pay the total amount for the Car in 12 monthly installments, that means, we need to pay monthly installment = 4000 / 12 = 333.33

                       Which if rounded off, we will require to pay $334 for the first 4 months and $333 for the next 8 months. (Note: Here, this monthly installment price does not include the interest to be paid )

Since, the interest payable is nominal interest of 6%, therefore, the interest amount per month becomes =    6% of 4000

= 6/100 x 4000

= $240

Therefore the monthly payment for the first four months would be ( 334+ 240 ) = $ 574

And the monthly payment for the next eight months would be = ( 333 + 240 ) = $ 573

Answer (b) : Until the fifth month, the total paid amount will be =

                            = 574 + 574 + 574+ 574 + 573

                             = $2,869

                    Now, from this amount, only 1669 is the principal amount, the rest is the interest paid.

Therefore, the remaining of the principal amount = $4,000 - $1669

                                                                                         = $2,331

Now, if we want to pay off the total of the remaining amount on the 6^th month, then the total payable amount would be = $2331 + $240

                                 = $2,571