# PreCalc Finance Project

## Expenses

Brent's salary is \$60,000 a year, how ever this figure does not represent his usable income. After federal tax with-holdings his actual income is roughly \$42,000 a year. Assuming he receives monthly paychecks, each month he should receive about \$3,500. Because Brent is currently making car payments we must subtract \$450 from his monthly income of \$3,500. This leaves Brent with \$3050. From \$3050 we subtract \$1500 for necessities. Brent's leftover income totals \$1550 which in this scenario will be the maximum monthly payment he can afford for a house.

## Loan Value

In this equation PV is equal to \$557,676 when the average rate is 4.625%. This translates into Brent paying \$557,676 at the end of the 30 year loan.

## The Decision

Brent was able to find many houses south of 435 that met his needs. The final decision came down to what he needs and what he doesn't need. Because Brent does not have a family he does not need many rooms and bath rooms. To keep the cost down Brent chose a 1,900 sq ft 3 bed 2.5 bath listed for exactly \$200,000. The house is in a nice neighborhood but could possibly benefit from light remodeling and updates.

## Minimum Monthly Payment

With a house listed at \$200,000 the recommended 20% down payment would bring the initial amount to be paid down to \$180,000 as we can see in the equation below. After solving the equations for X we find the minimum monthly payment to be \$500.29. This leaves Brent with a large disposable income. Because this is Brent's first house it is unlikely to be his last, with the large amount of money he will be saving by choosing a more modest option Brent will be able to move into a larger or nicer house in the future.

## Increased Monthly Payment

While choosing a more modest option will save Brent money, he may also save money by paying more than his minimum monthly payment. If Brent were to pay 15% more than the minimum (\$500.29) and pay \$575.33 a month he could save a substantial amount of money.

Once the equation below is solved for n and divided by 12 to find the monthly payment and the time the loan can now be paid off we find that it can be paid off in just over 26 years. By increasing the monthly payment by just 15% Brent is able to pay off the loan almost 4 years sooner.