Question
A bank account earns 3% interest per year. If you deposit $1,000 into the account, what equation would you use to determine how much will be in the account after 5 years?
A. y=1,000(1.03)
5
B. y=1,000(0.03)
5
C. y=5(0.03)
1,000
D. y=5(1.03)
1,000
A. y=1,000(1.03)
5
B. y=1,000(0.03)
5
C. y=5(0.03)
1,000
D. y=5(1.03)
1,000
Answers
GPT-4o mini
To determine how much will be in a bank account after 5 years with an initial deposit of $1,000 earning 3% interest per year, you need to use the formula for compound interest. The correct equation would be:
\[ y = P(1 + r)^t \]
Where:
- \( P \) is the principal amount (initial deposit),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years.
In this case:
- \( P = 1,000 \),
- \( r = 0.03 \) (3% expressed as a decimal),
- \( t = 5 \).
So the equation becomes:
\[ y = 1,000(1 + 0.03)^5 \]
or
\[ y = 1,000(1.03)^5 \]
Looking at the options provided, the closest match to this equation is:
**A. y = 1,000(1.03)^5**
Therefore, the correct answer is **A**.
\[ y = P(1 + r)^t \]
Where:
- \( P \) is the principal amount (initial deposit),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years.
In this case:
- \( P = 1,000 \),
- \( r = 0.03 \) (3% expressed as a decimal),
- \( t = 5 \).
So the equation becomes:
\[ y = 1,000(1 + 0.03)^5 \]
or
\[ y = 1,000(1.03)^5 \]
Looking at the options provided, the closest match to this equation is:
**A. y = 1,000(1.03)^5**
Therefore, the correct answer is **A**.