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\begin{tabular}{|c|c|c|c|c|}
\hline Principal & \begin{tabular}{l} Interest \\ Year 1 \end{tabular} & \begin{tabular}{l} Interest Year \\ 10 \end{tabular} & Interest Year 20 & \begin{tabular}{l} Total Savings After 20 \\ Years \end{tabular} \\
\hline \begin{tabular}{l} \[tex]$12,000 in Simple \\ Interest Account \end{tabular} & \begin{tabular}{l} \$[/tex]12,000 x \\ 5\% \\ = \[tex]$600 \\ = \$[/tex]12,600 \end{tabular} & \begin{tabular}{l} \[tex]$12,000 x 5\% \\ = \$[/tex]6000 \\ = \[tex]$18,000 \end{tabular} & \begin{tabular}{l} \$[/tex]12,000 x 5\% \\ = \[tex]$12000 \\ = \$[/tex]24,000 \end{tabular} & \begin{tabular}{l} \[tex]$12,000 + 20 years of \\ simple interest \\ = \$[/tex]24,000 \end{tabular} \\
\hline \begin{tabular}{l} \[tex]$12,000 in \\ Compound Interest \\ Account \end{tabular} & \begin{tabular}{l} \$[/tex]12,000 x \\ 5\% \\ = \[tex]$600 \\ = \$[/tex]12,600 \end{tabular} & \begin{tabular}{l} (\[tex]$12,000 + \\ \$[/tex]6,615.94) \\ = \[tex]$18,615.94 x \\ 5\% \\ = \$[/tex]19,546.74 \end{tabular} & \begin{tabular}{l} (\[tex]$12,000 + \\ \$[/tex]18,323.40) \\ = \[tex]$30,323.40 x \\ 5\% \\ = \$[/tex]31,839.57 \end{tabular} & \begin{tabular}{l} \[tex]$12,000 + 20 years \\ of compound interest \\ = \$[/tex]31,839.57 \end{tabular} \\
\hline
\end{tabular}

Patrick has \$12,000 saved for medical school from gifts and summer jobs. Because the cost of college has risen each year, Patrick knows he needs a savings account that will help him meet these increases. In the 10 remaining years before he receives his medical degree, which of the following would most help Patrick to meet these increases?

A. A checking account

B. A compound interest account

C. A high-risk investment

D. A simple interest account



Answer :

GinnyAnswer
To determine which type of savings account would be most beneficial for Patrick, we need to compare how much Patrick will save under both simple interest and compound interest after 10 years.

Simple Interest Calculation:

The formula for calculating simple interest is:
[tex]\[ \text{Simple Interest} = P \times r \times t \][/tex]

Where `P` is the principal amount, `r` is the annual interest rate, and `t` is the time in years.

Given:
- Principal ([tex]\(P\)[/tex]) = [tex]$12,000 - Annual interest rate (\(r\)) = 5% or 0.05 - Time (\(t\)) = 10 years 1. Calculate Simple Interest: \[ \text{Simple Interest} = 12000 \times 0.05 \times 10 \] \[ \text{Simple Interest} = 12000 \times 0.5 \] \[ \text{Simple Interest} = 6000 \] 2. Calculate Total Savings with Simple Interest: \[ \text{Total Savings} = \text{Principal} + \text{Simple Interest} \] \[ \text{Total Savings} = 12000 + 6000 \] \[ \text{Total Savings} = 18000 \] So, after 10 years, the total amount in a simple interest account will be $[/tex]18,000.

Compound Interest Calculation:

The formula for calculating compound interest is:
[tex]\[ A = P \left(1 + r\right)^t \][/tex]

Where `A` is the amount of money accumulated after n years, including interest.

Given:
- Principal ([tex]\(P\)[/tex]) = [tex]$12,000 - Annual interest rate (\(r\)) = 5% or 0.05 - Time (\(t\)) = 10 years 1. Calculate Total Savings with Compound Interest: \[ A = 12000 \left(1 + 0.05\right)^{10} \] \[ A = 12000 \left(1.05\right)^{10} \] \[ A = 12000 \times 1.62889 \] \[ A \approx 19546.74 \] So, after 10 years, the total amount in a compound interest account will be approximately $[/tex]19,546.74.

Comparison:

- Simple Interest Account: [tex]$18,000 after 10 years. - Compound Interest Account: Approximately $[/tex]19,546.74 after 10 years.

Conclusion:

The compound interest account yields a higher amount after 10 years compared to the simple interest account. Therefore, the compound interest account would most help Patrick meet the increasing costs of medical school.

Answer:
A compound interest account

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