Question
A+deposit+of+7,912+is+made+into+a+new+account+that+earns+5.75+simple+interest.+No+additional+deposits+or+withdrawals+will+be+made+for+2+years. Which amount is closest to the balance in the account at the end of 2 years?
Answers
GPT-4o mini
To calculate the balance in an account that earns simple interest, you can use the formula:
\[
A = P + I
\]
where:
- \( A \) is the total amount in the account after interest.
- \( P \) is the principal amount (initial deposit).
- \( I \) is the interest earned.
The formula for simple interest (\( I \)) is:
\[
I = P \times r \times t
\]
where:
- \( P \) is the principal (7,912),
- \( r \) is the interest rate (5.75% or 0.0575 when expressed as a decimal),
- \( t \) is the time in years (2 years).
First, calculate the interest earned over 2 years:
\[
I = 7,912 \times 0.0575 \times 2
\]
Now calculate:
\[
I = 7,912 \times 0.0575 \times 2 = 7,912 \times 0.115 = 910.88
\]
Next, find the total amount \( A \):
\[
A = 7,912 + 910.88 = 8,822.88
\]
Therefore, the amount closest to the balance in the account at the end of 2 years is approximately **$8,822.88**.
\[
A = P + I
\]
where:
- \( A \) is the total amount in the account after interest.
- \( P \) is the principal amount (initial deposit).
- \( I \) is the interest earned.
The formula for simple interest (\( I \)) is:
\[
I = P \times r \times t
\]
where:
- \( P \) is the principal (7,912),
- \( r \) is the interest rate (5.75% or 0.0575 when expressed as a decimal),
- \( t \) is the time in years (2 years).
First, calculate the interest earned over 2 years:
\[
I = 7,912 \times 0.0575 \times 2
\]
Now calculate:
\[
I = 7,912 \times 0.0575 \times 2 = 7,912 \times 0.115 = 910.88
\]
Next, find the total amount \( A \):
\[
A = 7,912 + 910.88 = 8,822.88
\]
Therefore, the amount closest to the balance in the account at the end of 2 years is approximately **$8,822.88**.