Questions: Find the future value of the loan. Round your answer to the nearest cent. P=200, r=9%, t=2 years The future value of the loan is

Solution Steps

To find the future value of the loan, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where:

• \(A\) is the future value of the loan
• \(P\) is the principal amount (\$200)
• \(r\) is the annual interest rate (9% or 0.09)
• \(t\) is the time the money is invested for (2 years)
• \(n\) is the number of times that interest is compounded per year (assuming it is compounded annually, \(n = 1\))

1. Identify the values for \(P\), \(r\), \(t\), and \(n\).
2. Substitute these values into the compound interest formula.
3. Calculate the future value \(A\).

We have the following values:

• Principal amount \( P = 200 \)
• Annual interest rate \( r = 0.09 \)
• Time in years \( t = 2 \)
• Compounding frequency \( n = 1 \)

The future value \( A \) of the loan can be calculated using the formula: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Substituting the identified values into the formula: \[ A = 200 \left(1 + \frac{0.09}{1}\right)^{1 \cdot 2} \]

Calculating the expression: \[ A = 200 \left(1 + 0.09\right)^{2} = 200 \left(1.09\right)^{2} \] Calculating \( (1.09)^{2} \): \[ (1.09)^{2} = 1.1881 \] Thus, \[ A = 200 \cdot 1.1881 = 237.62 \]

Final Answer