maria deposits \$50,000 into an account that pays 2\% interest per year, compounded annually.
john deposits \$50,000 into an account that also pays 2\% per year. but it is simple interest.

find the interest maria and john earn during each of the first three years.
then decide who earns more interest for each year.
assume there are no withdrawals and no additional deposits.

\begin{tabular}{|c|c|c|c|}
\hline
\textbf{year} & \textbf{interest maria earns (interest compounded annually)} & \textbf{interest john earns (simple interest)} & \textbf{who earns more interest?} \\
\hline
first & \$ & \$ & select \\
\hline
second & \$ & \$ & select \\
\hline
third & \$ & \$ & select \\
\hline
\end{tabular}

Question

maria deposits \$50,000 into an account that pays 2\% interest per year, compounded annually.
john deposits \$50,000 into an account that also pays 2\% per year. but it is simple interest.

find the interest maria and john earn during each of the first three years.
then decide who earns more interest for each year.
assume there are no withdrawals and no additional deposits.

\begin{tabular}{|c|c|c|c|}
\hline
\textbf{year} & \textbf{interest maria earns (interest compounded annually)} & \textbf{interest john earns (simple interest)} & \textbf{who earns more interest?} \\
\hline
first & \$ & \$ & select \\
\hline
second & \$ & \$ & select \\
\hline
third & \$ & \$ & select \\
\hline
\end{tabular}

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Compound Interest", "Simple Interest" ], "new_concepts": [], "current_concepts": [ "Compound Interest", "Simple Interest" ] } ## Calculate John's simple interest for each year $$ \begin{aligned} &P = 50000,\quad r = 0.02\ &I_{\text{John, Year 1}} = 50000 \times 0.02 = 1000\ &I_{\text{John, Year 2}} = 50000 \times 0.02 = 1000\ &I_{\text{John, Year 3}} = 50000 \times 0.02 = 1000 \end{aligned} $$ ## Calculate Maria's compound interest for each year $$ \begin{aligned} &A_0 = 50000\ &I_{\text{Maria, Year 1}} = 50000 \times 0.02 = 1000\ &A_1 = 50000 + 1000 = 51000\ &I_{\text{Maria, Year 2}} = 51000 \times 0.02 = 1020\ &A_2 = 51000 + 1020 = 52020\ &I_{\text{Maria, Year 3}} = 52020 \times 0.02 = 1040.40 \end{aligned} $$ ## Compare interest earned each year $$ \begin{aligned} &\text{Year 1: } 1000 = 1000 \implies \text{They earn the same amount}\ &\text{Year 2: } 1020 > 1000 \implies \text{Maria earns more}\ &\text{Year 3: } 1040.40 > 1000 \implies \text{Maria earns more} \end{aligned} $$ | Year | Interest Maria earns (Interest compounded annually) | Interest John earns (Simple interest) | Who earns more interest? | | :--- | :--- | :--- | :--- | | First | \$1,000 | \$1,000 | They earn the same amount | | Second | \$1,020 | \$1,000 | Maria earns more | | Third | \$1,040.40 | \$1,000 | Maria earns more | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Compound Interest" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate John's simple interest for each year

Calculate Maria's compound interest for each year

Compare interest earned each year

Answer:

Year	Interest Maria earns (Interest compounded annually)	Interest John earns (Simple interest)	Who earns more interest?
Second	\$1,020	\$1,000	Maria earns more
Third	\$1,040.40	\$1,000	Maria earns more