The Henley's took out a loan for 195,000 to purchase a home. At a 4.3% interest rate compounded annually ,how much interest will they have paid after 30 years? 471,259.24 Groundhog Day 429,305.61 the 4th of July 494,546.99 Valentine's Day 412,749.79 Labor Day

## Step 1: <br />Identify the given values:<br />- Principal amount, \( P = \$195,000 \)<br />- Interest rate, \( r = 4.3\% = 0.043 \) (converted to decimal)<br />- Number of times interest is compounded per year, \( n = 1 \) (annually)<br />- Time in years, \( t = 30 \)<br /><br />## Step 2:<br />Use the compound interest formula to calculate the amount after 30 years:<br />### \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]<br />Substitute the given values into the formula:<br />### \[ A = 195,000 \left(1 + \frac{0.043}{1}\right)^{1 \cdot 30} \]<br /><br />## Step 3:<br />Perform the calculation:<br />### \[ A = 195,000 \left(1 + 0.043\right)^{30} \]<br />### \[ A = 195,000 \left(1.043\right)^{30} \]<br />### \[ A = 195,000 \cdot 3.386 \]<br />### \[ A = 664,230 \]<br /><br />## Step 4:<br />Calculate the interest paid by subtracting the principal amount from the amount after 30 years:<br />### \[ \text{Interest} = A - P \]<br />### \[ \text{Interest} = 664,230 - 195,000 \]<br />### \[ \text{Interest} = 469,230 \]