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
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
Answers
GPT-4o mini
To find the total amount of the investment after 27 years with an annual compound interest, 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 your case:
- \( P = 15,000 \)
- \( r = 3.4\% = 0.034 \)
- \( t = 27 \)
Now, we can substitute these values into the formula:
\[
A = 15000(1 + 0.034)^{27}
\]
\[
A = 15000(1.034)^{27}
\]
Calculating \( (1.034)^{27} \):
\[
(1.034)^{27} \approx 2.526
\]
Now we can calculate \( A \):
\[
A \approx 15000 \times 2.526 \approx 37890
\]
Now rounding to the nearest cent, we find:
\[
A \approx 37890.00
\]
Since this was not an option, let’s recompute assuming there was an error in exponentiation:
Calculating \( (1.034)^{27} \) again more precisely:
1.034 raised to the power of 27 is approximately 2.502266.
Now, multiply:
\[
A = 15000 \times 2.502266 \approx 37534.00
\]
Still, let’s check the option against proper value calculations. Using a financial calculator or accurate software:
Ultimately, we arrive back at options during scrutiny.
The amounts are:
- $13,770.00
- $28,770.00
- $36,995.24
- $21,995.24
None matched exactly, but recalculating closely is essential. Therefore, the closest and valid post-iteration value that should have neighbours is:
- $36,995.24 aligns more closely (considering financial contexts).
Thus, the answer to the original question, based on investment longevity and general growth, is:
**$36,995.24** likely stands as the closest option in collective terms.
\[
A = P(1 + r)^t
\]
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 your case:
- \( P = 15,000 \)
- \( r = 3.4\% = 0.034 \)
- \( t = 27 \)
Now, we can substitute these values into the formula:
\[
A = 15000(1 + 0.034)^{27}
\]
\[
A = 15000(1.034)^{27}
\]
Calculating \( (1.034)^{27} \):
\[
(1.034)^{27} \approx 2.526
\]
Now we can calculate \( A \):
\[
A \approx 15000 \times 2.526 \approx 37890
\]
Now rounding to the nearest cent, we find:
\[
A \approx 37890.00
\]
Since this was not an option, let’s recompute assuming there was an error in exponentiation:
Calculating \( (1.034)^{27} \) again more precisely:
1.034 raised to the power of 27 is approximately 2.502266.
Now, multiply:
\[
A = 15000 \times 2.502266 \approx 37534.00
\]
Still, let’s check the option against proper value calculations. Using a financial calculator or accurate software:
Ultimately, we arrive back at options during scrutiny.
The amounts are:
- $13,770.00
- $28,770.00
- $36,995.24
- $21,995.24
None matched exactly, but recalculating closely is essential. Therefore, the closest and valid post-iteration value that should have neighbours is:
- $36,995.24 aligns more closely (considering financial contexts).
Thus, the answer to the original question, based on investment longevity and general growth, is:
**$36,995.24** likely stands as the closest option in collective terms.