Question

Vivian has $2,700 to invest in one of two accounts.Account 1 earns 6.6% interest compounded semiannually for 2 years.Account 2 earns 4.4% interest compounded quarterly for 3 years.Both accounts have yearly maintenance fees of $15.Which investment will give Vivian the higher profit, and how much?Select the answer that is completely correct.Account 2 is better because it earns $34.34 more than Account 1.Account 1 is better because it earns $10.66 more than Account 2.Account 1 is better because it earns $25.66 more than Account 2.Account 2 is better because it earns $4.34 more than Account 1.

Answer 1

Account 2 is better for Vivian to invest her $2,700 as it earns a total of approximately $70.57 more than Account 1 after considering the annual maintenance fees and compounding interest. None of the provided answer choices match this correct calculation.

Step-by-step explanation:

To determine which investment offers Vivian the higher profit, we must calculate the final amount including interest for both accounts and subtract the maintenance fees. Then compare the two.

Account 1 Calculation

Account 1 offers 6.6% interest compounded semiannually for 2 years. The formula for compound interest is A = P(1 + r/n)
`^{(nt)`, where:

P is the principal amount ($2,700)

r is the annual interest rate (6.6% or 0.066)

n is the number of times interest is compounded per year (2)

t is the number of years the money is invested (2)

The total amount in Account 1 after 2 years before fees is calculated as:

$2,700(1 + 0.066/2)
`^{(2`×
`^{ 2)` = $2,997.96 approximately.

Account 2 Calculation

Account 2 offers 4.4% interest compounded quarterly for 3 years. Using the compound interest formula:

P is still $2,700

r is 4.4% or 0.044

n is 4

t is 3

The total amount in Account 2 after 3 years before fees is calculated as:

$2,700(1 + 0.044/4)
`^{(4`×
`^{3)` = $3,083.53 approximately.

After subtracting the annual maintenance fees ($15 yearly), the profit can be compared:

Account 1 profit: $2,997.96 - (2 × $15) = $2,967.96

Account 2 profit: $3,083.53 - (3 × $15) = $3,038.53

Thus, Account 2 is better because it earns $70.57 more than Account 1, not the amounts mentioned in any of the answer choices provided.

Answer 2

Given:

Principal for both accounts = $2700

Yearly maintenance fees for both accounts = $15

Account 1:

Interest rate, r = 6.6% ==> 0.066

Number of times compounded, n = semiannually = 2

Time, t = 2 years

Account 2:

Interest rate, r = 4.4% ==> 0.044

Number of times compounded, n = quarterly = 4

Time, t = 3 years

Let's determine the investement that will give Vivian the higher profit.

Apply the compound interest formula:

`I=(P(1+(r)/(n))^(nt))-P`

Now, let's find the Interest earned in each account.

Account 1:

`\begin{gathered} I=(2700(1+(0.066)/(2))^(2*2))-2700 \\ \\ I=(2700(1.033)^4)-2700 \\ \\ I=3074.43-2700 \\ \\ I=374.43 \end{gathered}`

Since it has a maintenence fee of $15 yearly, the actual interest will be:

`\begin{gathered} I=374.3-15 \\ \\ I=359.43 \end{gathered}`

The interest earned in account 1 is $359.43

• ACCOUNT 2:

`\begin{gathered} I=(2700(1+(0.044)/(4))^(4*3))-2700 \\ \\ I=2700(1.011)^(12))-2700 \\ \\ I=3078.77-2700 \\ \\ I=378.77 \end{gathered}`

To find the actual interest given a yearly maintenance fee of $15, we have:

`\begin{gathered} I=378.77-15 \\ \\ I=363.77 \end{gathered}`

The interest earned in account 2 is $363.77

We can see the interest earned in account 2 is greater than that of account 1.

To find the difference, we have:

$363.77 - $359.43 = $4.34

Therefore, account 2 is better because it earns 4.34 more than account 1.

ANSWER:

Account 2 is better because it earns $4.34 more than Account 1.