Question
Cali invests $9,400 at 6.2% for 7 years. What is the expected maximum value of this investment? Round to the nearest hundred.(1 point)
expected value =$
expected value =$
Answers
GPT-4o mini
To calculate the expected maximum value of the investment using the compound interest formula, we use:
\[
A = P(1 + r)^t
\]
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 number of years the money is invested or borrowed.
In this case:
- \( P = 9,400 \)
- \( r = 6.2\% = 0.062 \)
- \( t = 7 \)
Now we can plug in the values:
\[
A = 9400(1 + 0.062)^7
\]
Calculating \( (1 + 0.062)^7 \):
\[
1 + 0.062 = 1.062
\]
\[
(1.062)^7 \approx 1.484812
\]
Now we calculate \( A \):
\[
A \approx 9400 \times 1.484812 \approx 13935.6308
\]
Rounding to the nearest hundred:
\[
A \approx 13900
\]
Therefore, the expected maximum value of the investment is:
\[
\text{Expected value} = \$13,900
\]
\[
A = P(1 + r)^t
\]
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 number of years the money is invested or borrowed.
In this case:
- \( P = 9,400 \)
- \( r = 6.2\% = 0.062 \)
- \( t = 7 \)
Now we can plug in the values:
\[
A = 9400(1 + 0.062)^7
\]
Calculating \( (1 + 0.062)^7 \):
\[
1 + 0.062 = 1.062
\]
\[
(1.062)^7 \approx 1.484812
\]
Now we calculate \( A \):
\[
A \approx 9400 \times 1.484812 \approx 13935.6308
\]
Rounding to the nearest hundred:
\[
A \approx 13900
\]
Therefore, the expected maximum value of the investment is:
\[
\text{Expected value} = \$13,900
\]