What is the monthly payment for a $750,000 mortgage with a 25-year amortization at 5.70% compounded semi-annually?

What is the monthly payment for a $750,000 mortgage with a 25-year amortization at 5.70% compounded semi-annually?

• A. $4,599.75
• B. $4,502.13
• C. $4,345.67
• D. $4,712.10

Answer: (A)

To determine the monthly payment for a $750,000 mortgage with a 25-year amortization at an interest rate of 5.70% compounded semi-annually, it’s important to first convert the semi-annual interest rate to a monthly interest rate, since mortgage payments are typically calculated on a monthly basis. The nominal interest rate of 5.70% compounded semi-annually needs to be adjusted to reflect a monthly payment schedule. To do this, the effective monthly interest rate is calculated as follows: 1. Divide the annual rate by 2 to find the semi-annual rate: 5.70% / 2 = 2.85%. 2. Convert the semi-annual rate to an effective monthly rate using the formula for effective interest rate conversion: - (1 + semi-annual rate)^(1/6) - 1 - This results in an approximate monthly interest rate of 0.473268%. Now, using the effective interest rate, we can apply the mortgage payment formula: \[ M = P \frac{r(1+r)^n}{(1+r)^n-1} \] Where: - M is the total monthly mortgage payment - P is the principal loan amount ($

To determine the monthly payment for a $750,000 mortgage with a 25-year amortization at an interest rate of 5.70% compounded semi-annually, it’s important to first convert the semi-annual interest rate to a monthly interest rate, since mortgage payments are typically calculated on a monthly basis.

The nominal interest rate of 5.70% compounded semi-annually needs to be adjusted to reflect a monthly payment schedule. To do this, the effective monthly interest rate is calculated as follows:

1. Divide the annual rate by 2 to find the semi-annual rate: 5.70% / 2 = 2.85%.

2. Convert the semi-annual rate to an effective monthly rate using the formula for effective interest rate conversion:

• (1 + semi-annual rate)^(1/6) - 1

• This results in an approximate monthly interest rate of 0.473268%.

Now, using the effective interest rate, we can apply the mortgage payment formula:

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

Where:

• M is the total monthly mortgage payment

• P is the principal loan amount ($