If a 30-year mortgage has monthly payments of $1,156.62 and an interest rate of 5.9%, what was the original mortgage amount?

If a 30-year mortgage has monthly payments of $1,156.62 and an interest rate of 5.9%, what was the original mortgage amount?

• A. $165,000
• B. $184,500
• C. $188,000
• D. $195,000

Answer: (D)

To determine the original mortgage amount for a fixed-rate mortgage given the monthly payment, interest rate, and loan term, we can use the formula for the monthly payment on a mortgage: \[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \] Where: - \(M\) is the monthly payment - \(P\) is the loan principal (original mortgage amount) - \(r\) is the monthly interest rate (annual rate divided by 12) - \(n\) is the total number of payments (loan term in months) In this case, the monthly payment \(M\) is \$1,156.62, the annual interest rate is 5.9%, and the loan term is 30 years, which means \(n = 30 \times 12 = 360\) months. The monthly interest rate \(r\) converts the annual rate from a percentage to a decimal and divides it by 12: \[ r = \frac{5.9\%}{100} \div 12 = 0.00491667 \] Now we can rearrange the mortgage payment formula to solve for \(P\): \

To determine the original mortgage amount for a fixed-rate mortgage given the monthly payment, interest rate, and loan term, we can use the formula for the monthly payment on a mortgage:

[

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

]

Where:

• (M) is the monthly payment

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

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

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

In this case, the monthly payment (M) is $1,156.62, the annual interest rate is 5.9%, and the loan term is 30 years, which means (n = 30 \times 12 = 360) months. The monthly interest rate (r) converts the annual rate from a percentage to a decimal and divides it by 12:

[

r = \frac{5.9%}{100} \div 12 = 0.00491667

]

Now we can rearrange the mortgage payment formula to solve for (P):

\