Respuesta :
To find the interest rate, we need to use the simple interest formula:
\[ I = P \times r \times t \]
Where:
- \( I \) is the interest,
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time the money is invested or borrowed for, in years.
From the information provided, we know that Vince deposited $4,000 and after two years the account held $5,040. So, the interest \( I \) earned can be calculated by:
\[ I = Total \, Amount - Principal \, Amount \]
\[ I = 5,040 - 4,000 \]
\[ I = 1,040 \]
We know the principal amount \( P \) is $4,000 and the time \( t \) is 2 years. Now we can plug these values into the formula and solve for the rate \( r \).
\[ 1,040 = 4,000 \times r \times 2 \]
Now, let's solve for \( r \):
\[ r = \frac{1,040}{(4,000 \times 2)} \]
\[ r = \frac{1,040}{8,000} \]
\[ r = 0.13 \]
To express the interest rate as a percentage, we multiply the decimal by 100:
\[ r = 0.13 \times 100 \]
\[ r = 13\% \]
Therefore, the interest rate is 13%.
\[ I = P \times r \times t \]
Where:
- \( I \) is the interest,
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time the money is invested or borrowed for, in years.
From the information provided, we know that Vince deposited $4,000 and after two years the account held $5,040. So, the interest \( I \) earned can be calculated by:
\[ I = Total \, Amount - Principal \, Amount \]
\[ I = 5,040 - 4,000 \]
\[ I = 1,040 \]
We know the principal amount \( P \) is $4,000 and the time \( t \) is 2 years. Now we can plug these values into the formula and solve for the rate \( r \).
\[ 1,040 = 4,000 \times r \times 2 \]
Now, let's solve for \( r \):
\[ r = \frac{1,040}{(4,000 \times 2)} \]
\[ r = \frac{1,040}{8,000} \]
\[ r = 0.13 \]
To express the interest rate as a percentage, we multiply the decimal by 100:
\[ r = 0.13 \times 100 \]
\[ r = 13\% \]
Therefore, the interest rate is 13%.
