You want to purchase a new car in 5 years and expect the car to cost ​$32,000. Your bank offers a plan with a guaranteed APR of 6.5 % if you make regular monthly deposits. How much should you deposit each month to end up with ​$32,000 in 5 ​years?You should invest ​$ each month.​(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as​ needed.)

Accepted Solution

Answer:You should deposit 533.33 dollars each monthStep-by-step explanation:The total amount to be payed after 5 years for the car can be expressed as;Cost of car after 5 years=Principal amount+Interest amountwhere;Cost of car after 5 years=$32,000Principal amount=PInterest amount=Principal×rate×Number of yearsInterest amount=P×(6.5/100)×5=0.325 Preplacing;32,000=P+0.325 p1.325 P=32,000P=32,000/1.325P=24,150.9434Amount to deposit each year=Total cost of car after 5 years/number of yearswhere;Total cost of car after 5 years=$32,000Number of years=5replacing;Amount to deposit per year=32,000/5=$6,400Amount to deposit each month=Amount to deposit per year/number of months in a yearwhere;Amount to deposit per year=$6,400Number of months in a year=12 monthsreplacing;Amount to deposit each month=6,400/12=533.33You should deposit 533.33 dollars each month