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

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.

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 - 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 -
`800(1 + 0.03)^(t)`

Pam equation is -
`800(1 + 0.04)^(t)`

Now,

1.)

For initial investment , Put t = 0

⇒B =
`800(1 + 0.03)^(0) = 800(1) = 800`

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

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 =
`800(1 + 0.03)^(5) = 800(1.03)^(5) = 800(1.1593) = 927.42`

P =
`800(1 + 0.04)^(5) = 800(1.04)^(5) = 800(1.2166) = 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.