Question

Determine the outstanding principal of the given mortgage. (Assume monthly interest payments and compounding periods.) HINT [See Example 7.] (Round your answer to the nearest cent.)

A $450,000, 30-year, 3.2% mortgage after 25 years

Answer 1

Explanation:

To determine the outstanding principal of the given mortgage after 25 years, we need to use the formula for the remaining balance on a mortgage:

B = L[(1 + c)^n - (1 + c)^t]/[(1 + c)^n - 1]

where:

B = remaining balance or outstanding principal

L = original loan amount = $450,000

c = monthly interest rate = 3.2% / 12 = 0.002666667

n = total number of payments = 30 years * 12 months per year = 360

t = number of payments made = 25 years * 12 months per year = 300

Plugging in these values, we get:

B = $450,000[(1 + 0.002666667)^360 - (1 + 0.002666667)^300]/[(1 + 0.002666667)^360 - 1]

B = $187,852.13

Therefore, the outstanding principal of the mortgage after 25 years is $187,852.13.