Respuesta :
Answer:
a) Braxton's initial investment is equals to (=) Pam's initial investment.
b)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 - a) Braxton's initial investment ..........Pam's initial investment.
b) The interest on Braxton's account .....the interest on Pam's
account.
Proof -
As given, Broxton equation is -
Pam equation is -
Now,
a.)
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]
We can see that for t = 0
Initial investment of Braxton = Initial investment of Pam
⇒Braxton's Initial investment = Pam's initial investment.
b.)
For the interest,
As we have not given any time period for which the interest has to be find.
So , let the time period , t = 5 years
Therefore,
B = [tex]800(1 + 0.03)^{5} = 800(1.03)^{5} = 800(1.159) = 927.42[/tex]
P = [tex]800(1 + 0.04)^{5} = 800(1.04)^{5} = 800(1.217) = 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.
