Question
Brenda deposited $2,059 in an account earning 1% interest compounded annually.
To the nearest cent, how much will she have in 1 year?
To the nearest cent, how much will she have in 1 year?
Answers
GPT-4o mini
To calculate the amount Brenda will have in her account after one year with compounded interest, you can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial deposit).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed.
In Brenda's case:
- \(P = 2059\)
- \(r = 0.01\) (1% expressed as a decimal)
- \(n = 1\)
Now, substituting the values into the formula:
\[
A = 2059(1 + 0.01)^1
\]
\[
A = 2059(1.01)
\]
\[
A = 2059 \times 1.01 = 2079.59
\]
So, to the nearest cent, Brenda will have **$2,079.59** in her account after 1 year.
\[
A = P(1 + r)^n
\]
where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial deposit).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed.
In Brenda's case:
- \(P = 2059\)
- \(r = 0.01\) (1% expressed as a decimal)
- \(n = 1\)
Now, substituting the values into the formula:
\[
A = 2059(1 + 0.01)^1
\]
\[
A = 2059(1.01)
\]
\[
A = 2059 \times 1.01 = 2079.59
\]
So, to the nearest cent, Brenda will have **$2,079.59** in her account after 1 year.