Fritz Benjamin buys a car costing 15800 He agrees to make pa

Fritz Benjamin buys a car costing $15800. He agrees to make payments at the end of each monthly period for 6 years. He pays 9.6% interest, compounded monthly. What is the amount of each payment? Find the total amount of interest Fritz will pay.

Solution

Given that

Cost of car P = $15800

Time t = 6 years

Iterest rate r = 9.6 % = 0.096

We know that

The amount of each payment compounded monthly A = P (1 + (r / n) ) ^nt

Where n = number of compoundings per year = 12

  A = p (1 + r / n) ^nt

= $15800 ( 1 + ( 0.096 / 12) ) ^12x6

= $15800 ( 1 +(1/125) ) ^12x6

= $15800 ( 126/125) ^12x6

= $15800 x 1.775

= $28045

A = $28045

Total amonut to be paid after 6 yrs, A = $28045

Amount to be paid at the end of each month =  $28045/ 12 = $ 2337

Total amount of interest = A-P

                                  = $ 28045 - $ 15800

                                  = $ 12245