Question

Braxton has money in a savings account. The equation B = 800(1+0.03)'.

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 = 800(1 + 0,04) can be

used to calculate the amount of money in dollars, P, Pam has in her account after t years

since opening the account.

Choose from the drop down menus to correctly complete each sentence.

Braxton's initial investment Choose...

Pam's initial investment.

The interest on Braxton's account Choose...

the interest on Pam's account.

Answer 1

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.

Explanation:

Given - Braxton has money in a savings account. The equation

B =
`800(1 + 0.03)^(t)` 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=
`800(1 + 0.04)^(t)` 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 =
`800(1 + 0.03)^(0) = 800(1) = 800`

P =
`800(1 + 0.04)^(0) = 800(1) = 800`

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 =
`800(1 + 0.03)^(5) = 800(1.03)^(5) = 800(1.159) = 927.42`

P =
`800(1 + 0.04)^(5) = 800(1.04)^(5) = 800(1.217) = 973.32`

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.