MTH $115-$ GENERAL EDUCATION MATHEMATICS

PROJECT $-$ CHAPTER $10$

PROJECT #$1($Ch$10-$ Mortgages$)$

Name

Date:

$-20$

Score

The Smiths are purchasing their first home. They are a two$-$person household with pets but no

children. They fell in love with a house that is listed at $$180,000$ and want to make an offer.

Before they do$,$ they want to consider the financial responsibilities of owning a house.

Part $1$: Down Payment and Mortgage

They are planning to make a $10\%$ down payment. $(2$ points$)$

a$.$ Determine the amount of the down payment.

b$.$ Determine the amount of the mortgage after they make the down payment.

Part $2$: A $15-$Year vs$.$ a $30-$Year Fixed mortgage

The Smiths really want to pay off their house as fast as possible, and are interested in a

$15-$year fixed mortgage at an interest rate of $3\mathrm{.}2\%.$ Determine the monthly payment for

principal and interest after they make the down payment. $(2$ points$)$

The Smiths realize the $15-$year mortgage may be out of their budget, and are also willing

to consider a $30-$year fixed mortgage at a slightly higher interest rate of $4\mathrm{.}1\%.$

Determine the monthly payment for principal and interest after they make the down

payment. $(2$ points$)$

MTH $115-$ GENERAL EDUCATION MATHEMATICS

PROJECT $-$ CHAPTER $10$

Part $3$: More about the $30-$Year Fixed mortgage

They have a combined income of $$80,000$ per year, which means that their combined

post$-$tax $($gross$)$ take$-$home pay is approximately $$4800$ per month. Their car is paid off

and they do not currently have any other fixed monthly payments to consider.

Determine $28\%$ of the Smiths adjusted monthly income. Remember, this is the

maximum they can afford. $(2$ points$)$

Part $4$: Other Financial Considerations

The Smiths have been researching strategies for a monthly budget. They have decided

to use the $50/30/20$ simple budget framework they found on

nerdwallet.com. $50\%$ of

their budget is supposed to go to needs, $30\%$ is for wants, and $20\%$ is for a combination

of savings and debt repayment. Remember, their post$-$tax monthly income is $$4800.(2$

points$)$

a$.$ Needs: What is $50\%$ of their monthly income?

b$.$ Wants: What is $30\%$ of their monthly income?

c$.$ Savings$/$Debt Repayment: What is $20\%$ of their monthly income?

They make a list of their needs for their monthly budget. $(3$ points$)$

Their monthly needs include: $($some values are estimations$)$

a$.$ What is the sum of their monthly needs?

b$.$ Their needs make up what percent of their $$4800$ post$-$tax income?

MTH $115-$ GENERAL EDUCATION MATHEMATICS

PROJECT $-$ CHAPTER $10$

As part of their $20\%$ savings and debt repayment mentioned in the budget model, they

plan to invest the difference of the monthly principal and interest payments for $15-$year

mortgages and $30-$year mortgages from numbers $2$ and $3$ into an annuity. $(3$ points$)$

a$.$ Determine the difference in the payments.

b$.$ Assume that the difference in monthly payments is invested in an ordinary

annuity each month at a rate of $2\%$ compounded monthly for $30$ years.

Determine the value of the investment in $30$ years.

Part $5$: Conclusion $($Use additional paper if needed.$)$

The Smiths ask for your opinion $-$ should they make an offer on the house? $(5$ points$)$

Yes or no$?$ Explain.

Are there any additional comments or advice you would give them? Explain.