Question
The Walkers have a mortgage of 189000 amortized over 25 years at 6.7% compounded I biweekly with a 4-year term. The mortgage is renewed for another 4-year term at 8.9% compounded biweekly . Determine the new monthly payment.
Solution
3.4
(241 Votes)
Hank
Master ยท Tutor for 5 years
Answer
### $1242.56
Explanation
## Step 1: Calculate the bi-weekly interest rate for the first term.### The annual interest rate is 6.7%, and it is compounded biweekly (26 times a year). Therefore, the bi-weekly interest rate is
.## Step 2: Calculate the number of payments in the first term.### The first term is 4 years, and there are 26 bi-weekly payments per year. So, the total number of payments in the first term is
.## Step 3: Calculate the bi-weekly payment for the first term.### Using the formula for mortgage payment:
, where
,
, and
(total payments over 25 years).
.## Step 4: Calculate the outstanding balance after the first term.### The outstanding balance can be calculated using the formula:
, where
(number of payments in the first term).
.## Step 5: Calculate the bi-weekly interest rate for the second term.### The annual interest rate for the second term is 8.9%, compounded biweekly. The bi-weekly interest rate is
.## Step 6: Calculate the number of payments remaining after the first term.### Since the amortization period is 25 years, and the first term is 4 years, there are
years remaining. The number of bi-weekly payments remaining is
.## Step 7: Calculate the bi-weekly payment for the second term.### Using the mortgage payment formula with the new interest rate and remaining balance:
.## Step 8: Calculate the new monthly payment.### Since there are approximately 26 bi-weekly payments in a year, and 12 months in a year, the monthly payment is approximately
.