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You have just applied for and been approved for a [tex]$\$[/tex]175,000[tex]$ mortgage. The rate quoted to you by the lender is $[/tex]5.5\%[tex]$ for a 30-year fixed mortgage. Use the provided table to determine how much of your first month's payment goes towards the principal.

\ \textless \ strong\ \textgreater \ Monthly Payments per $[/tex]\[tex]$1000$[/tex] of Mortgage

\begin{tabular}{c|c|c|c|c|}
\hline
\begin{tabular}{l}
Interest \\
Rate (\%)
\end{tabular} & 10 Years & 20 Years & 30 Years & 40 Years \\
\hline
5.0 & 10.61 & 6.60 & 5.37 & 4.83 \\
\hline
5.5 & 10.86 & 6.88 & 5.68 & 5.16 \\
\hline
6.0 & 11.11 & 7.17 & 6.00 & 5.51 \\
\hline
6.5 & 11.36 & 7.46 & 6.33 & 5.86 \\
\hline
\end{tabular}

a. [tex]$\$[/tex]191.92[tex]$
b. $[/tex]\[tex]$190.23$[/tex]
c. [tex]$\$[/tex]187.32[tex]$
d. $[/tex]\[tex]$184.88$[/tex]

Please select the best answer from the choices provided.


Sagot :

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]