Questions: You have 12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money. a. 3.99 % compounded monthly b. 4 % compounded quarterly c. 4.175 % compounded annually d. 4.2 % simple interest

Solution Steps

For the investment option with \(3.99\%\) compounded monthly, we use the formula for compound interest:

\[ FV_a = P \left(1 + \frac{r_a}{n_a}\right)^{n_a \cdot t} \]

Substituting the values:

\[ FV_a = 12000 \left(1 + \frac{0.0399}{12}\right)^{12 \cdot 8} \approx 16503.58 \]

For the investment option with \(4\%\) compounded quarterly, we apply the compound interest formula:

\[ FV_b = P \left(1 + \frac{r_b}{n_b}\right)^{n_b \cdot t} \]

Substituting the values:

\[ FV_b = 12000 \left(1 + \frac{0.04}{4}\right)^{4 \cdot 8} \approx 16499.29 \]

For the investment option with \(4.175\%\) compounded annually, we again use the compound interest formula:

\[ FV_c = P \left(1 + \frac{r_c}{n_c}\right)^{n_c \cdot t} \]

Substituting the values:

\[ FV_c = 12000 \left(1 + \frac{0.04175}{1}\right)^{1 \cdot 8} \approx 16645.21 \]

For the investment option with \(4.2\%\) simple interest, we use the simple interest formula:

\[ FV_d = P(1 + rt_d) \]

Substituting the values:

\[ FV_d = 12000 \left(1 + 0.042 \cdot 8\right) \approx 16032.00 \]

Now we compare the future values calculated for each option:

• \(FV_a \approx 16503.58\)
• \(FV_b \approx 16499.29\)
• \(FV_c \approx 16645.21\)
• \(FV_d \approx 16032.00\)

The maximum future value is \(FV_c\), which corresponds to the investment option with \(4.175\%\) compounded annually.

Final Answer