Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
The equity will be the value of the house today minus the present value of the remaining mortgage payments.
We can start with the value of the house. If the house was originally valued in $80,000 and appreciated at 9% per year during 7 seven years, we can calculate the present value as:
[tex]\begin{gathered} PV=80000\cdot(1+0.09)^7 \\ PV=80000\cdot1.09^7 \\ PV\approx80000\cdot1.828 \\ PV\approx146243.13 \end{gathered}[/tex]Now we can calculate the present value of the mortgage payments as an annuity.
The payments are monthly (m = 12), with an annual rate of 12% (r = 0.12). The amount paid monthly is $500 and there are 48 remaining payments (m*t = 48), so we can calculate the annuity as:
[tex]\begin{gathered} PV=M\cdot\frac{1-(1+\frac{r}{m})^{-m\cdot t}}{\frac{r}{m}} \\ PV=500\cdot\frac{1-(1+\frac{0.12}{12})^{-48}}{\frac{0.12}{12}} \\ PV=500\cdot\frac{1-(1.01)^{-48}}{0.01} \\ PV\approx500\cdot\frac{1-0.62026}{0.01} \\ PV\approx500\cdot\frac{0.37974}{0.01} \\ PV\approx500\cdot37.974 \\ PV\approx18986.98 \end{gathered}[/tex]Then, if we substract the mortgage present value from the present value of the house, we get the equity:
[tex]\begin{gathered} E=PV_{h\text{ouse}}-PV_{\text{mortgage}} \\ E=146243.13-18986.98 \\ E=127256.15 \end{gathered}[/tex]Answer: the present equity in the house is $127,256.15
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
