Respuesta :
Answer:
Braxton's initial investment is equals to (=) Pam's initial investment.
The interest on Braxton's account is less than (< ) the interest on Pam's account.
Step-by-step explanation:
Given - Braxton has money in a savings account. The equation
B = [tex]800(1 + 0.03)^{t}[/tex] can be used to calculate the amount of money
in dollars, B, Braxton has in his account after t years since opening
the account.
Pam also has money in a savings account. The equation
P=[tex]800(1 + 0.04)^{t}[/tex] can be used to calculate the amount of money in
dollars, P, Pam has in her account after t years since opening the
account.
To find - Braxton's initial investment ..........Pam's initial investment.
The interest on Braxton's account .....the interest on Pam's account.
Proof -
As given, Broxton equation is - [tex]800(1 + 0.03)^{t}[/tex]
Pam equation is - [tex]800(1 + 0.04)^{t}[/tex]
Now,
1.)
For initial investment , Put t = 0
⇒B = [tex]800(1 + 0.03)^{0} = 800(1) = 800[/tex]
P = [tex]800(1 + 0.04)^{0} = 800(1) = 800[/tex]
As for t = 0
Braxton's equation , B = Pam's equation,P
⇒Braxton's Initial investment = Pam's initial investment.
2.)
For the interest,
As we don not have time for which the interest has to be check.
So , let the time period = 5 years
Therefore,
B = [tex]800(1 + 0.03)^{5} = 800(1.03)^{5} = 800(1.1593) = 927.42[/tex]
P = [tex]800(1 + 0.04)^{5} = 800(1.04)^{5} = 800(1.2166) = 973.32[/tex]
Now,
Interest on Braxton's account = 927.42 - 800 = 127.42 ≈ 127
Interest on Pam's account = 973.32 - 800 = 173.32 ≈ 173
∴ we get
The interest on Braxton's account is less than the interest on Pam's account.
