To determine the interest savings in Question 45, we need to calculate the total interest paid over two different loan terms for the $512,000 home purchase from Question 41, specifically comparing a 30-year loan to a 15-year loan.

Steps to Calculate the Interest Savings:

1. Determine the Loan Amount and Interest Rate:

   • From Question 41, the home costs $512,000, and with a 20% down payment, the financed amount is: $512,000 \times (1 - 0.20) = 512,000 \times 0.80 = 409,600$
   • The interest rate is 5.1%.

2. Calculate Monthly Payment for 30-Year Loan:

   • Use the loan amount of $409,600, a term of 30 years (360 months), and an interest rate of 5.1% (monthly rate = 5.1% / 12).
   • Monthly payment formula: [ M = P \frac{r(1 + r)^n}{(1 + r)^n -