Answer :
Let's work through this problem step-by-step.
1. Determine the monthly mortgage payment:
- The loan amount is [tex]$175,000. - The interest rate is 5.5% per year for a 30-year fixed mortgage. - The monthly payment per $[/tex]1,000 of mortgage for a 5.5% interest rate over 30 years is given as [tex]$5.68. To find the total monthly payment: \[ \text{Total Monthly Payment} = \left(\frac{\$[/tex]175,000}{\[tex]$1,000}\right) \times 5.68 = 175 \times 5.68 = \$[/tex]994.00
\]
2. Calculate the interest portion of the first monthly payment:
- The annual interest rate is 5.5%, so the monthly interest rate is:
[tex]\[ \text{Monthly Interest Rate} = \frac{5.5\%}{12} = \frac{0.055}{12} = 0.0045833\ \text{(approximately)} \][/tex]
The interest for the first month is:
[tex]\[ \text{First Month's Interest} = \$175,000 \times 0.0045833 = \$802.08\ \text{(approximately)} \][/tex]
3. Calculate the principal portion of the first month's payment:
- The principal portion is the total monthly payment minus the interest portion.
[tex]\[ \text{First Month's Principal} = \$994.00 - \$802.08 = \$191.92 \][/tex]
From these calculations, the principal portion of your first month's payment will be closest to the amount given in option (a):
[tex]\[ \boxed{\$191.92} \][/tex]
1. Determine the monthly mortgage payment:
- The loan amount is [tex]$175,000. - The interest rate is 5.5% per year for a 30-year fixed mortgage. - The monthly payment per $[/tex]1,000 of mortgage for a 5.5% interest rate over 30 years is given as [tex]$5.68. To find the total monthly payment: \[ \text{Total Monthly Payment} = \left(\frac{\$[/tex]175,000}{\[tex]$1,000}\right) \times 5.68 = 175 \times 5.68 = \$[/tex]994.00
\]
2. Calculate the interest portion of the first monthly payment:
- The annual interest rate is 5.5%, so the monthly interest rate is:
[tex]\[ \text{Monthly Interest Rate} = \frac{5.5\%}{12} = \frac{0.055}{12} = 0.0045833\ \text{(approximately)} \][/tex]
The interest for the first month is:
[tex]\[ \text{First Month's Interest} = \$175,000 \times 0.0045833 = \$802.08\ \text{(approximately)} \][/tex]
3. Calculate the principal portion of the first month's payment:
- The principal portion is the total monthly payment minus the interest portion.
[tex]\[ \text{First Month's Principal} = \$994.00 - \$802.08 = \$191.92 \][/tex]
From these calculations, the principal portion of your first month's payment will be closest to the amount given in option (a):
[tex]\[ \boxed{\$191.92} \][/tex]
