10. Mr. and Mrs. Rainer took out a \( \$ 240,000 \) loan to purchase their home. If the interest rate on the loan is \( 1.2 \% \) compounded bimonthly, how much interest will they have paid after 30 years? \( P=240,000 \)

To calculate the interest paid after 30 years on the loan, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial loan amount). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is borrowed for. Here, \( P = 240,000 \), \( r = 0.012 \), \( n = 6 \) (since it is bimonthly), and \( t = 30 \). Calculating \( A \): \[ A = 240,000 \left(1 + \frac{0.012}{6}\right)^{6 \times 30} \] \[ A = 240,000 \left(1 + 0.002\right)^{180} \] \[ A = 240,000 \times (1.002)^{180} \] \[ A ≈ 240,000 \times 1.399 \] \[ A ≈ 335,760 \] Now, to find the interest paid, we subtract the principal from the total amount: Interest = \( A - P \) Interest = \( 335,760 - 240,000 \) Interest ≈ \( 95,760 \) So, Mr. and Mrs. Rainer will have paid approximately \( \$95,760 \) in interest after 30 years. Now let’s dive into more exciting insights about mortgages and loans! Buying your first home can feel like a scary rollercoaster ride with all the ups and downs! Did you know that the average homeowner stays in their home for about 13 years before moving? That means many people experience the wonders of mortgage payments while dreaming of their next adventure. Don’t forget: refinancing can save you money too, especially if interest rates drop! Home loans can seem overwhelming, but they’re a ticket to building equity over time! With every mortgage payment, you’re not just paying interest; a portion is chipping away at the loan principal too! Remember to crunch some numbers on different loan types—fixed-rate vs. adjustable-rate—before you leap. And avoid a common mistake: underestimate the costs of property taxes and insurance when budgeting for your home!