Part III: Selling the House

Suppose that after living in the house for $10$ years, you decide to sell it$.$ The economy experiences ups and downs, but in general the value of real estate increases over time.

Recall the original purchase price $($$$2337\mathrm{.}00)30$ year loan

Original purchase price $($from Part $1)=$$Correct

To approximate the future value of an investment such as real estate, you will use the compounded interest formula:

PN$=$P$0(1+$rk$)$Nk

This is just an approximation, so we'll use an annual compounding period $($so$,$ k$=1).$

Find the future value of the home $10$ years after you purchased it assuming a $6\%$ interest rate. Use the full purchase price of the home from the previous problem $($Question $1)$ as the principal $($or initial value, P$0)$ in the compound interest formula.

Future value of home$=$$ $418521\mathrm{.}11$

This "Future value" is the price you will sell the house for after you've owned it for ten years. Now you will answer the question of whether or not you have made or lost money with this investment. You will need several pieces of information in order to answer the question. You will need the amount of your down payment $($from Part $1),$ the amount you paid toward the mortgage over ten years $($your monthly payment from Question $1$ times the number of payments$),$ and finally, the amount of principal you still owe on the mortgage.

Down payment$=$$ $233\mathrm{.}70$

Mortgage paid over $10$ years$=$$ $157462\mathrm{.}80$

To find the principal balance on the mortgage, you will use the Loan Formula:

P$0=$ d$(1(1+$rk$)$Nk$)($rk$)$

$($In this formula, d is the monthly payment and r is the annual interest rate expressed as a decimal from Part I, so r$=$; k$=12,$ and N is the number of years remaining on the loan.$)$

Principal balance on mortgage after $10$ years$=$$

To determine whether or not you've made or lost money, you must compare the "expenses" $($down payment $+$ mortgage paid $+$ principal balance$)$ to the "return" $($future value of the home$).$

Find the total "expenses".

Expenses$=$$

After $10$ years, did you lose or gain money from selling the house? Answer:

How much $($did you lose or gain$)?$ Answer:$