Question

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.)

Answer 1

You should deposit 533.33 dollars each month

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 amount

where;

Cost of car after 5 years=$32,000

Principal amount=P

Interest amount=Principal×rate×Number of years

Interest amount=P×(6.5/100)×5=0.325 P

replacing;

32,000=P+0.325 p

1.325 P=32,000

P=32,000/1.325

P=24,150.9434

Amount to deposit each year=Total cost of car after 5 years/number of years

where;

Total cost of car after 5 years=$32,000

Number of years=5

replacing;

Amount to deposit per year=32,000/5=$6,400

Amount to deposit each month=Amount to deposit per year/number of months in a year

where;

Amount to deposit per year=$6,400

Number of months in a year=12 months

replacing;

Amount to deposit each month=6,400/12=533.33

You should deposit 533.33 dollars each month