Answer:
a
The value of the CD when it matures is [tex]V_{CD} =[/tex]$ 8,480
b
Bill receive from his friend [tex]z =[/tex]$8273.2
Step-by-step explanation:
From the question we are told that
The price of the car is [tex]P =[/tex]$8000
The certificate of deposit is [tex]CD = 9 \ months[/tex]
The annual interest is [tex]a =[/tex]8%
The value CD when it matures can be mathematically represented as
[tex]V_{CD} = P + \frac{P * a * \frac{t}{12} }{100}[/tex]
substituting values
[tex]V_{CD} = 8000 + \frac{8000 * 0.8 * \frac{9}{12} }{100}[/tex]
substituting values we have
[tex]V_{CD} =[/tex]$ 8,480
Let assume bill received z dollars from his friend
Now the total amount after three months which is the duration of the loan is mathematically evaluated as
[tex]K = z + \frac{z * 0.10 * \frac{3}{12} }{100}[/tex]
Now since the amount after three month is equivalent to the value of CD as we are told from the question that Bill agreed his friend receives the CD as payback we have that
[tex]K = 8480 = z + \frac{z * 0.10 * \frac{3}{12} }{100}[/tex]
=> [tex]8480 = z [1 + \frac{1}{40} ][/tex]
=> [tex]z = \frac{40}{41} * 8480[/tex]
[tex]z =[/tex]$8273.2
