Using the information above, [latex]P = $153,899[/latex], [latex]r = 0.0421[/latex] and [latex]t = 20[/latex]. Substituting those values into the formula [latex]pmt=\frac{P\times\frac{r}{12}\times(1+\frac{r}{12})^{12\times t}}{(1+\frac{r}{12})^{12\times t}−1}[/latex] and calculating, we find the payment is:

[latex]\begin{array}{ll}
PMT && = \frac{P\times\frac{r}{12}\times(1+\frac{r}{12})^{12\times t}}{(1+\frac{r}{12})^{12\times t}−1} \\
&& =\frac{$153,899\times\frac{0.0421}{12}\times(1+\frac{0.0421}{12})^{12\times 20}}{(1+\frac{0.0421}{12})^{12\times 20}−1} \\
&& =\frac{$153,899\times(.0035)\times(1.0035)^{240}}{(1.0035)^{240}−1} \\
&& =\frac{$1,245.874451}{1.312972331} \\
&& = \$948.90 \\
\end{array}[/latex]

His mortgage payment is [latex]$948.90[/latex].
Note: Answers may vary slightly depending on how numbers were rounded.

To find the total paid over the life of the mortgage, use the formula [latex]T=pmt\times12\times t[/latex]. To calculate this, the payment must be found. Using the information above, [latex]P = $225,879[/latex], [latex]r = 0.0491[/latex] and [latex]t = 15[/latex]. Substituting those values into the formula [latex]pmt=\frac{P\times\frac{r}{12}\times(1+\frac{r}{12})^{12\times t}}{(1+\frac{r}{12})^{12\times t}−1}[/latex] and calculating, we find the payment is:

[latex]\begin{array}{ll}
PMT && = \frac{P\times\frac{r}{12}\times(1+\frac{r}{12})^{12\times t}}{(1+\frac{r}{12})^{12\times t}−1} \\
&& =\frac{$$225,879\times\frac{0.0491}{12}\times(1+\frac{0.0491}{12})^{12\times 15}}{(1+\frac{0.0491}{12})^{12\times 15}−1} \\
&& =\frac{$225,879\times(.004091\overline{6})\times(1.004091\overline{6})^{180}}{(1.004091\overline{6})^{180}−1} \\
&& =\frac{$1927.439709}{1.085473955 } \\
&& = \$1,775.67 \\
\end{array}[/latex]

Using the mortgage payment of [latex]$1,775.67[/latex] and [latex]t = 15[/latex] years in the formula [latex]T=pmt\times12\times t[/latex], the total that Arthur will pay for the mortgage is [latex]$319,618.80[/latex].
Note: Answers may vary slightly depending on how numbers were rounded.

We just found that the total that Arthur will pay for the [latex]$225,879[/latex] mortgage is [latex]$319,618.80[/latex]. (See previous example for the worked solution).

Subtracting those we find the cost of financing [latex]CoF=T−P = $319,618.80−$225,879=$93,739.80[/latex].
Note: Answers may vary slightly depending on how numbers were rounded.

Using the payment function to find Destiny’s mortgage payments, [latex]pmt=\frac{P\times\frac{r}{12}\times(1+\frac{r}{12})^{12\times t}}{(1+\frac{r}{12})^{12\times t}−1}[/latex], with [latex]P = $159,195.50[/latex], [latex]r = 0.0575[/latex] and [latex]t = 30[/latex], her payments are:

[latex]\begin{array}{ll}
PMT && = \frac{P\times\frac{r}{12}\times(1+\frac{r}{12})^{12\times t}}{(1+\frac{r}{12})^{12\times t}−1} \\
&& =\frac{$159,195.50\times\frac{0.0575}{12}\times(1+\frac{0.0575}{12})^{12\times 30}}{(1+\frac{0.0575}{12})^{12\times 30}−1} \\
&& = \$929.02 \\
\end{array}[/latex]

Destiny also pays into escrow [latex]\frac{1}{12}[/latex] of her property taxes per month. Her property taxes are [latex]5.42\%[/latex] of the assessed value of [latex]$100,000[/latex], which comes to [latex]0.0542\times$100,000=$5,420[/latex]. This is an annual tax, so she pays [latex]\frac{1}{12}[/latex] of that each month, or [latex]$451.67[/latex]. Destiny’s home insurance is [latex]$843[/latex] per [latex]6[/latex] months, so each month she pays [latex]$140.50[/latex] for insurance.

Adding these together, her monthly payment is [latex]$929.02+$451.67+$140.50=$1,521.19[/latex]. This is quite a bit more than the [latex]$929.02[/latex] for the principal and interest.

1. Reading at the top of the table, we see the interest rate is [latex]6.1\%[/latex].
2. Reading from the top of the table or from the column labeled Payment, we see the payments are [latex]$1,383.61[/latex] per month.
3. In the row for payment [latex]235[/latex], we see that the amount that goes to principal is [latex]$730.38[/latex].
4. In the row for payment [latex]215[/latex], we see that the amount that goes to interest is [latex]$723.66[/latex].
5. In the row for payment [latex]227[/latex], we see the remaining balance is [latex]$133,513.05[/latex].
6. Payment [latex]225[/latex].