a viweekly Determine the new monthly payment. Determine the difference in the interest paid over a 25-year period on a 259,000 mortgage at 7.5% compounded monthly and at 11.5% compounde d monthlv

## Step 1: Calculate the monthly payment for the 7.5% mortgage<br />### We use the formula for monthly mortgage payments: $M = P \frac{r(1+r)^n}{(1+r)^n - 1}$, where $M$ is the monthly payment, $P$ is the principal loan amount, $r$ is the monthly interest rate, and $n$ is the total number of payments. Here, $P = \$259,000$, $r = \frac{0.075}{12} = 0.00625$, and $n = 25 \times 12 = 300$.<br />$M = 259000 \times \frac{0.00625(1+0.00625)^{300}}{(1+0.00625)^{300}-1} \approx \$1928.61$<br /><br />## Step 2: Calculate the total interest paid for the 7.5% mortgage<br />### Total interest paid is the total amount paid minus the principal. Total amount paid is the monthly payment multiplied by the number of payments.<br />Total amount paid $= \$1928.61 \times 300 = \$578,583$<br />Total interest paid $= \$578,583 - \$259,000 = \$319,583$<br /><br />## Step 3: Calculate the monthly payment for the 11.5% mortgage<br />### We use the same formula as in Step 1, but with $r = \frac{0.115}{12} \approx 0.009583$.<br />$M = 259000 \times \frac{0.009583(1+0.009583)^{300}}{(1+0.009583)^{300}-1} \approx \$2662.80$<br /><br />## Step 4: Calculate the total interest paid for the 11.5% mortgage<br />### We use the same method as in Step 2.<br />Total amount paid $= \$2662.80 \times 300 = \$798,840$<br />Total interest paid $= \$798,840 - \$259,000 = \$539,840$<br /><br />## Step 5: Calculate the difference in interest paid<br />### The difference is the interest paid on the 11.5% mortgage minus the interest paid on the 7.5% mortgage.<br />Difference $= \$539,840 - \$319,583 = \$220,257$