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Chris invests $15,000 in a retirement account with an annual compound interest rate of 3.4%. Find the total amount of the inves...Question
Chris invests $15,000 in a retirement account with an annual compound interest rate of 3.4%. Find the total amount of the investment after 27 years. Round answers to the nearest cent (hundredth). *Remember to use your STAAR Reference Sheet for support! (1 point) Responses $13,770.00 $13,770.00 $28,770.00 $28,770.00 $36,995.24 $36,995.24 $21,995.24 $21,995.24 Skip to navigation
Answers
GPT-4o mini
To calculate the total amount of the investment after 27 years with an annual compound interest rate of 3.4%, we can use the formula for compound interest:
\[
A = P(1 + r)^t
\]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(t\) is the time the money is invested for, in years.
In this case:
- \(P = 15,000\)
- \(r = 3.4\% = 0.034\)
- \(t = 27\)
Plugging these values into the formula, we get:
\[
A = 15000(1 + 0.034)^{27}
\]
Calculating \(1 + 0.034\):
\[
1 + 0.034 = 1.034
\]
Now raise \(1.034\) to the power of \(27\):
\[
1.034^{27} \approx 2.487610
\]
Now, multiply this by the principal amount:
\[
A \approx 15000 \times 2.487610 \approx 37314.15
\]
So after rounding to the nearest cent, the total amount of the investment after 27 years is approximately:
\[
A \approx 37314.15
\]
Thus, the options provided do not include this result, suggesting a verification or adjustment is necessary in choices provided or potentially in the interest calculation. However, the calculated value is approximately **$37,314.15**.
Always ensure to verify source data and recheck calculations or available choices. Consider confirming with financial growth calculators or further clarify options provided.
\[
A = P(1 + r)^t
\]
Where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(t\) is the time the money is invested for, in years.
In this case:
- \(P = 15,000\)
- \(r = 3.4\% = 0.034\)
- \(t = 27\)
Plugging these values into the formula, we get:
\[
A = 15000(1 + 0.034)^{27}
\]
Calculating \(1 + 0.034\):
\[
1 + 0.034 = 1.034
\]
Now raise \(1.034\) to the power of \(27\):
\[
1.034^{27} \approx 2.487610
\]
Now, multiply this by the principal amount:
\[
A \approx 15000 \times 2.487610 \approx 37314.15
\]
So after rounding to the nearest cent, the total amount of the investment after 27 years is approximately:
\[
A \approx 37314.15
\]
Thus, the options provided do not include this result, suggesting a verification or adjustment is necessary in choices provided or potentially in the interest calculation. However, the calculated value is approximately **$37,314.15**.
Always ensure to verify source data and recheck calculations or available choices. Consider confirming with financial growth calculators or further clarify options provided.