Question
Leroy deposited $8,000 in an account earning 5% interest compounded annually. To the nearest cent, how much will he have in 2 years?
Answers
GPT-4o mini
To calculate the future value of an investment with compounded interest, you can use the formula:
\[
A = P(1 + r)^t
\]
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 Leroy's case:
- \( P = 8000 \)
- \( r = 0.05 \) (which is 5% expressed as a decimal)
- \( t = 2 \)
Now, we can substitute these values into the formula:
\[
A = 8000(1 + 0.05)^2
\]
Calculating the expression inside the parentheses first:
\[
1 + 0.05 = 1.05
\]
Now we raise \( 1.05 \) to the power of 2:
\[
1.05^2 = 1.1025
\]
Now substitute back into the equation:
\[
A = 8000 \times 1.1025
\]
Calculating this gives:
\[
A = 8816
\]
Thus, the amount Leroy will have in 2 years is:
\[
\boxed{8816.00}
\]
\[
A = P(1 + r)^t
\]
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 Leroy's case:
- \( P = 8000 \)
- \( r = 0.05 \) (which is 5% expressed as a decimal)
- \( t = 2 \)
Now, we can substitute these values into the formula:
\[
A = 8000(1 + 0.05)^2
\]
Calculating the expression inside the parentheses first:
\[
1 + 0.05 = 1.05
\]
Now we raise \( 1.05 \) to the power of 2:
\[
1.05^2 = 1.1025
\]
Now substitute back into the equation:
\[
A = 8000 \times 1.1025
\]
Calculating this gives:
\[
A = 8816
\]
Thus, the amount Leroy will have in 2 years is:
\[
\boxed{8816.00}
\]