In a mortgage of $178,500 over 30 years with a monthly payment of $1,128.24, what is the interest rate?

To determine the interest rate in a mortgage of $178,500 over 30 years with a monthly payment of $1,128.24, one typically uses the formula for the monthly payment of a fixed-rate mortgage. The payment can be calculated using the loan amount (P), the monthly interest rate (r), and the total number of payments (n), which in this case is the number of months over 30 years (30 years × 12 months/year = 360 months). The formula is expressed as:

[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} ]

In this context, we need to find the value of r (the monthly interest rate) that satisfies the equation with the known values of M ($1,128.24), P ($178,500), and n (360).

The solution process involves iterative methods or financial calculators since algebraically isolating r in the formula is complex. This calculation often results in a monthly interest rate that must then be converted into an annual percentage rate (APR) by multiplying the monthly rate by 12.

After computations are conducted (whether through a financial calculator, spreadsheet, or numerical methods), the calculated