What was the original mortgage amount for a 25-year mortgage with monthly payments of $1,253.37 at a 6.25% interest rate?

To determine the original mortgage amount for a 25-year mortgage with monthly payments of $1,253.37 at a 6.25% interest rate, we can use the formula for the present value of an annuity, which is commonly used in mortgage calculations.

The formula for the present value of an annuity is:

[

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

]

where:

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

• ( PMT ) is the monthly payment,

• ( r ) is the monthly interest rate (annual interest rate divided by 12), and

• ( n ) is the total number of payments (number of years times 12).

In this case:

• The monthly payment ( PMT = 1,253.37 ),

• The annual interest rate is 6.25%, so the monthly interest rate ( r = 6.25% / 12 = 0.520833% ) or 0.00520833 when expressed as a decimal,

• The number of payments for a 25-year mortgage is ( n =