Question
Briar is thinking about investing $7,800 at 4.1% for 3 years. What is the maximum value Briar can expect this investment to achieve? Round to the nearest hundred.(1 point)
maximum value =$
maximum value =$
Answers
GPT-4o mini
To calculate the maximum value of Briar's investment, we will use the formula for compound interest, assuming the interest is compounded annually:
\[
A = P(1 + r)^n
\]
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).
- \( n \) is the number of years the money is invested.
Given:
- \( P = 7,800 \)
- \( r = 4.1\% = 0.041 \)
- \( n = 3 \)
Now we can substitute these values into the compound interest formula:
\[
A = 7,800 \times (1 + 0.041)^3
\]
\[
A = 7,800 \times (1.041)^3
\]
\[
A = 7,800 \times 1.1277281 \quad (\text{approximating } (1.041)^3)
\]
\[
A \approx 8,806.08
\]
Now, rounding to the nearest hundred:
\[
\text{maximum value} \approx 8,800
\]
Therefore, the maximum value Briar can expect this investment to achieve is **$8,800**.
\[
A = P(1 + r)^n
\]
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).
- \( n \) is the number of years the money is invested.
Given:
- \( P = 7,800 \)
- \( r = 4.1\% = 0.041 \)
- \( n = 3 \)
Now we can substitute these values into the compound interest formula:
\[
A = 7,800 \times (1 + 0.041)^3
\]
\[
A = 7,800 \times (1.041)^3
\]
\[
A = 7,800 \times 1.1277281 \quad (\text{approximating } (1.041)^3)
\]
\[
A \approx 8,806.08
\]
Now, rounding to the nearest hundred:
\[
\text{maximum value} \approx 8,800
\]
Therefore, the maximum value Briar can expect this investment to achieve is **$8,800**.