To determine the amount of money Adam will owe after one year with simple interest, we can use the formula for simple interest:
\[ I = P \times r \times t \]
Where:
- \(I\) is the interest
- \(P\) is the principal amount (the initial amount borrowed)
- \(r\) is the interest rate (as a decimal)
- \(t\) is the time (in years)
In this case:
- \(P = 5600\) dollars
- \(r = 0.042\) (which is 4.2% expressed as a decimal)
- \(t = 1\) year
First, we calculate the interest for one year:
\[ I = 5600 \times 0.042 \times 1 = 235.2 \]
Now, to find the total amount \(x\) that Adam owes after one year, we add the interest to the principal:
\[ x = P + I = 5600 + 235.2 = 5835.2 \]
Thus, the equation that represents the amount of money Adam will owe in one year, if no payments are made, is:
\[ x = 5600 + 5600(0.042)(1) \]
Looking at the options you provided, the correct choice is:
x = 5,600 + 5,600(0.042)(1)