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

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:

$I=(P(1+\frac{r}{n})^{nt})-P$

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

Account 1:

$\begin{gathered} I=(2700(1+\frac{0.066}{2})^{2\times2})-2700 \\ \\ I=(2700(1.033)^4)-2700 \\ \\ I=3074.43-2700 \\ \\ I=374.43 \end{gathered}$

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:

$\begin{gathered} I=(2700(1+\frac{0.044}{4})^{4\times3})-2700 \\ \\ I=2700(1.011)^{12})-2700 \\ \\ I=3078.77-2700 \\ \\ I=378.77 \end{gathered}$

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.