If a 20-year mortgage with an interest rate of 6.15% has monthly payments of $1,305.20, what was the original mortgage amount?

To determine the original mortgage amount based on the monthly payment, interest rate, and term, we can use the formula for the monthly payment on an amortizing loan:

[

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

]

where:

• ( M ) is the monthly payment,

• ( P ) is the loan principal (the original mortgage amount),

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

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

In this scenario, the monthly payment ( M ) is $1,305.20. The annual interest rate is 6.15%, which gives a monthly interest rate as follows:

[

r = \frac{6.15%}{12} = \frac{0.0615}{12} \approx 0.005125

]

The term of the mortgage is 20 years, equating to:

[

n = 20 \times 12 = 240 \text{ months}

]

To find the original mortgage amount ( P ), we can rearrange the formula:

[