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?

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?

• A. $180,000
• B. $184,500
• C. $195,000
• D. $203,000

Answer: (A)

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: \[

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:

[