Question
Miranda puts $400.00 into an account to use for school expenses. The account earns 14% interest, compounded annually. How much will be in the account after 7 years?
Answers
GPT-4o mini
To determine how much will be in the account after 7 years, we can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial money).
- \( r \) = the annual interest rate (decimal).
- \( n \) = the number of years the money is invested or borrowed.
In this case:
- \( P = 400 \)
- \( r = 0.14 \) (14% as a decimal)
- \( n = 7 \)
Now we can substitute these values into the formula:
\[
A = 400(1 + 0.14)^7
\]
Calculating \( 1 + 0.14 \):
\[
1 + 0.14 = 1.14
\]
Now raised to the power of 7:
\[
1.14^7 \approx 2.5023 \quad \text{(using a calculator)}
\]
Now multiply this with the principal amount:
\[
A \approx 400 \times 2.5023 \approx 1001.92
\]
Thus, the amount in the account after 7 years will be approximately **$1001.92**.
\[
A = P(1 + r)^n
\]
where:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial money).
- \( r \) = the annual interest rate (decimal).
- \( n \) = the number of years the money is invested or borrowed.
In this case:
- \( P = 400 \)
- \( r = 0.14 \) (14% as a decimal)
- \( n = 7 \)
Now we can substitute these values into the formula:
\[
A = 400(1 + 0.14)^7
\]
Calculating \( 1 + 0.14 \):
\[
1 + 0.14 = 1.14
\]
Now raised to the power of 7:
\[
1.14^7 \approx 2.5023 \quad \text{(using a calculator)}
\]
Now multiply this with the principal amount:
\[
A \approx 400 \times 2.5023 \approx 1001.92
\]
Thus, the amount in the account after 7 years will be approximately **$1001.92**.