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How much money will be spent in interest alone over the course of the 4\% 30-year mortgage described in the table?

Mortgage Payments

\begin{tabular}{|r|r|}
\hline \multicolumn{2}{|r|}{ Principal: [tex]$\$[/tex] 200,000.00[tex]$} \\
\hline Interest Rate & Monthly Payment \\
\hline $[/tex]3 \%[tex]$ & $[/tex]\[tex]$ 843$[/tex] \\
\hline [tex]$4 \%$[/tex] & [tex]$\$[/tex] 955[tex]$ \\
\hline $[/tex]5 \%[tex]$ & $[/tex]\[tex]$ 1074$[/tex] \\
\hline
\end{tabular}

[tex]$\$[/tex][?]$


Sagot :

To determine how much money will be spent in interest alone over the course of the 4% 30-year mortgage, we follow a series of steps:

1. Principal Amount: The initial loan amount is \[tex]$200,000. 2. Monthly Payment: The monthly payment for a 4% interest rate mortgage is \$[/tex]955.

3. Number of Payments: Since it is a 30-year mortgage, and there are 12 months in a year, the total number of monthly payments is:
[tex]\[ 30 \text{ years} \times 12 \text{ months/year} = 360 \text{ months} \][/tex]

4. Total Payment Over 30 Years: To find out the total amount paid over the term of the mortgage, we multiply the monthly payment by the number of months:
[tex]\[ 955 \text{ dollars/month} \times 360 \text{ months} = 343,800 \text{ dollars} \][/tex]

5. Interest Paid: The total interest paid is the total amount paid over the mortgage term minus the principal. We then subtract the principal amount from the total payment:
[tex]\[ 343,800 \text{ dollars (total payment)} - 200,000 \text{ dollars (principal)} = 143,800 \text{ dollars} \][/tex]

Hence, the amount spent in interest alone over the course of the 4% 30-year mortgage is \$143,800.
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