Question
I have $500 in a savings account with a 4% annual interest rate compounded annually. How much will I have in the account after 5 years, rounded to the nearest cent?
Answers
GPT-4o mini
To calculate the amount in the savings account after 5 years with an annual interest rate of 4% compounded annually, you 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 number of years the money is invested or borrowed.
In your case:
- \(P = 500\)
- \(r = 0.04\)
- \(t = 5\)
Plugging these values into the formula:
\[
A = 500(1 + 0.04)^5
\]
Calculating \(1 + 0.04\):
\[
1 + 0.04 = 1.04
\]
Now raising it to the power of 5:
\[
1.04^5 \approx 1.2166529 \quad (\text{using a calculator})
\]
Now, multiplying by the principal amount:
\[
A \approx 500 \times 1.2166529 \approx 608.32645
\]
Rounding to the nearest cent:
\[
A \approx 608.33
\]
Therefore, after 5 years, you will have approximately **$608.33** in the account.
\[
A = P(1 + r)^t
\]
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 your case:
- \(P = 500\)
- \(r = 0.04\)
- \(t = 5\)
Plugging these values into the formula:
\[
A = 500(1 + 0.04)^5
\]
Calculating \(1 + 0.04\):
\[
1 + 0.04 = 1.04
\]
Now raising it to the power of 5:
\[
1.04^5 \approx 1.2166529 \quad (\text{using a calculator})
\]
Now, multiplying by the principal amount:
\[
A \approx 500 \times 1.2166529 \approx 608.32645
\]
Rounding to the nearest cent:
\[
A \approx 608.33
\]
Therefore, after 5 years, you will have approximately **$608.33** in the account.