What was the original amount of a mortgage with monthly payments of $1,179.92 at 6.8% for 25 years?

To determine the original amount of a mortgage based on the monthly payment, interest rate, and loan term, you would typically use the formula for calculating the present value of an annuity. The monthly payment amount and the interest rate can be used to find the initial loan amount, known as the principal.

In this case, the monthly payment is $1,179.92, the annual interest rate is 6.8% (which translates to a monthly interest rate of ( \frac{6.8%}{12} = 0.00566667 )), and the term of the mortgage is 25 years (or 300 months).

Using the present value of an annuity formula:

[

PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)

]

Where:

• ( PV ) is the present value of the mortgage (original loan amount),

• ( PMT ) is the monthly payment,

• ( r ) is the monthly interest rate (as a decimal),

• ( n ) is the total number of payments (loan term in months).

Substituting in the values:

[

PV = 1179.92 \