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
Answers
GPT-4o mini
To calculate the total amount of an investment with compound interest, you can use the formula:
\[
A = P(1 + r)^n
\]
Where:
- \( A \) is the total amount after time \( n \),
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal),
- \( n \) is the number of years the money is invested.
In this case:
- \( P = 15,000 \)
- \( r = 3.4\% = 0.034 \)
- \( n = 27 \)
Now plug these values into the formula:
\[
A = 15000(1 + 0.034)^{27}
\]
Calculate \( (1 + 0.034)^{27} \):
\[
1.034^{27} \approx 2.565216
\]
Now substitute this value back into the equation:
\[
A \approx 15000 \times 2.565216 \approx 38478.24
\]
So after rounding to the nearest cent, the total amount in the account after 27 years would be:
\[
A \approx 38,478.24
\]
Since the total amount of the investment does not match any of the provided options, it seems there is a misunderstanding in reading or calculating the final answer. Is there a misinterpretation in the values? Based on the calculations, \( A \) should indeed be around \( 38,478.24 \), which is not present in the choices given.
Let's ensure our calculations were exact. Double-check the computation using \( r = 0.034 \) over 27 years:
Calculating again:
1. Calculate \( (1 + 0.034)^{27} \):
\[
1.034^{27} \approx 2.565216
\]
2. Multiply by the principal:
\[
A \approx 15000 \times 2.565216 \approx 38478.24
\]
Indeed, it seems consistent. The conclusion remains that none of the provided options fit. Please double-check for options or re-evaluate any provided choices that may have been overlooked.
\[
A = P(1 + r)^n
\]
Where:
- \( A \) is the total amount after time \( n \),
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (in decimal),
- \( n \) is the number of years the money is invested.
In this case:
- \( P = 15,000 \)
- \( r = 3.4\% = 0.034 \)
- \( n = 27 \)
Now plug these values into the formula:
\[
A = 15000(1 + 0.034)^{27}
\]
Calculate \( (1 + 0.034)^{27} \):
\[
1.034^{27} \approx 2.565216
\]
Now substitute this value back into the equation:
\[
A \approx 15000 \times 2.565216 \approx 38478.24
\]
So after rounding to the nearest cent, the total amount in the account after 27 years would be:
\[
A \approx 38,478.24
\]
Since the total amount of the investment does not match any of the provided options, it seems there is a misunderstanding in reading or calculating the final answer. Is there a misinterpretation in the values? Based on the calculations, \( A \) should indeed be around \( 38,478.24 \), which is not present in the choices given.
Let's ensure our calculations were exact. Double-check the computation using \( r = 0.034 \) over 27 years:
Calculating again:
1. Calculate \( (1 + 0.034)^{27} \):
\[
1.034^{27} \approx 2.565216
\]
2. Multiply by the principal:
\[
A \approx 15000 \times 2.565216 \approx 38478.24
\]
Indeed, it seems consistent. The conclusion remains that none of the provided options fit. Please double-check for options or re-evaluate any provided choices that may have been overlooked.