11.5% compounded monthly. The Wilson's purchased a home for 350000 The put 25% down and took out a mortgage for the rest. The mortgage had an interest rate ate of 13.5% compounded of 13.5% biweekly for an amortization period of 20 years . At the end of their 7-year term, the Wilsons renewed their mortgage at 8.25% compounded biweekly for a 5-year term and then renewed their mortgage again at 9.3% compounded biweekly for the remaining 8 years. a) What was the monthly payment during the 7-year term? b) What was the monthly payment during the 5-year term? b) What was the monthly payment during the 8-year term? d) How much interest did the Wilsons pay over the 20 years?

## Step 1: Calculate the Mortgage Principal<br />### The Wilsons put down 25% of $350,000, so their down payment was $0.25 \times 350000 = \$87500$. The mortgage principal is the purchase price minus the down payment: $350000 - 87500 = \$262500$.<br /><br />## Step 2: Calculate the Monthly Payment for the 7-Year Term<br />### The interest rate is 13.5% compounded biweekly. The biweekly interest rate is $\frac{0.135}{26} = 0.0051923$. The number of biweekly payments in 7 years is $7 \times 26 = 182$. The mortgage payment formula is $P = \frac{rPV}{1-(1+r)^{-n}}$, where P is the payment, r is the interest rate per period, PV is the present value (loan amount), and n is the number of periods. Therefore, the biweekly payment is $P = \frac{0.0051923 \times 262500}{1 - (1 + 0.0051923)^{-182}} = \$1878.73$. The monthly payment is $1878.73 \times \frac{26}{12} \approx \$4065.97$.<br /><br />## Step 3: Calculate the Monthly Payment for the 5-Year Term<br />### First, we need to calculate the outstanding balance after the 7-year term. The outstanding balance formula is $B = PV(1+r)^n - P\frac{(1+r)^n - 1}{r}$. $B = 262500(1+0.0051923)^{182} - 1878.73\frac{(1+0.0051923)^{182}-1}{0.0051923} \approx \$220969.79$. The new interest rate is 8.25% compounded biweekly, so the biweekly rate is $\frac{0.0825}{26} = 0.003173$. The number of biweekly payments in 5 years is $5 \times 26 = 130$. The biweekly payment is $P = \frac{0.003173 \times 220969.79}{1 - (1 + 0.003173)^{-130}} = \$1934.40$. The monthly payment is $1934.40 \times \frac{26}{12} \approx \$4192.87$.<br /><br />## Step 4: Calculate the Monthly Payment for the 8-Year Term<br />### The outstanding balance after the 5-year term is $B = 220969.79(1+0.003173)^{130} - 1934.40\frac{(1+0.003173)^{130}-1}{0.003173} \approx \$151436.05$. The new interest rate is 9.3% compounded biweekly, so the biweekly rate is $\frac{0.093}{26} = 0.003577$. The number of biweekly payments in 8 years is $8 \times 26 = 208$. The biweekly payment is $P = \frac{0.003577 \times 151436.05}{1 - (1 + 0.003577)^{-208}} = \$1006.79$. The monthly payment is $1006.79 \times \frac{26}{12} \approx \$2180.63$.<br /><br />## Step 5: Calculate the Total Interest Paid<br />### Total amount paid during the 7-year term: $1878.73 \times 182 = \$342230.86$. Total amount paid during the 5-year term: $1934.40 \times 130 = \$251472$. Total amount paid during the 8-year term: $1006.79 \times 208 = \$209386.32$. Total amount paid: $342230.86 + 251472 + 209386.32 = \$803089.18$. Total interest paid: $803089.18 - 262500 = \$540589.18$.