6-45: Bill Anderson buys a car every 2 years as follows: initially he makes a do

Question

6-45: Bill Anderson buys a car every 2 years as follows: initially he makes a down payment of $6,000 on a $15,000 car. The balance is paid in 24 equal monthly payments with annual interest at 12%. When he has made the last payment on the loan, he trades in the 2-year old car for $6,000 on a new $15,000 car, and the cycle begins over again.

Doug Jones decided on a different purchase plan. He thought he would be better off if he paid $15,000 cash for a new car. Then he would make a monthly deposit in a savings account so that, at the end of 2-years, he would have $9,000 in the account. The $9,000 plus the $6,000 trade-in value of the car woll allow Doug to replace his 2-year-old car by paying $9,000 for a new one. The bank pays 6% interest, compounded quarterly.

(a) What is Bill Anderson's monthly payment to payoff the loan on the car?
(b) After he purchased the new car for cash, how much per month should Doug Jones deposit in his savings account to have enough money for the next car 2 years hence?
(c) Why is Doug's monthly savings account deposit smaller than Bill's payment?

Explanation / Answer

(a)

A    = $9,000 (A/P, 1%, 24) = $9,000 (0.0471) = $423.90/month

(b)

Note that interest is compounded quarterly

A’         = $9,000 (A/F, 1.5%, 8) = $9,000 (0.1186) = $1,067.40

Monthly Deposit     = ½ of A’     = ($1,067.40)/3    = $355.80/mo

(c)   In part (a) Bill Anderson’s monthly payment includes an interest payment on the loan. The sum of his 24 monthly payments will exceed $9,000

In part (b) Doug James’ savings account monthly deposit earns interest for him that helps to accumulate the $9,000. The sum of Doug’s 24 monthly deposits will be less than $9,000.

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