# Jenny's First Home

### Pre-Calculus Finance Project

## Home Choice

Jenny's home is located at 107 W Elm Street in Olathe, Kansas 66061. With 3 bedrooms and 2 bathrooms, she will have ample space and even a future possibility of roommates. It is a $50,000 home, but her savings over the past 3 years will amount to enough to make a $10,000 (20%) down payment, and her monthly income will cover the payments with plenty of room to spare!

## Monthly Income

With her salary of $40,000 a year working as a bank teller, the ending monthly income works out to be $868.17, as shown below.

40,000 x .30 = 28,000 per year because of tax

28,000/ 12= 2,333.33 per month

Her student loan of $20,000 is calculated by the equation:

20,000= R(1-(1+(.068/12)^ -120) / (.068/12)) *6.8% interest rate and monthly payments over 10 years

This gives her the monthly payments of $230.16 for 10 years.

Monthly costs include her student loan payment of $230.16, $230 for her car payment, $305 for food, $250 for fun, $250 for misc., and $200 to save.

The equation 2,333.33 - (230.16 + 230 + 305 + 250 + 250 + 200) = 868.17, shows that Jenny has **$868,17** each month to spend on house payments.

## Amount Borrowed

Because of the $10,000 down payment, Jenny will need to pay off $40,000 over time.

The most she could borrow from the bank with a 4.625% interest rate is $45,000, with monthly payments of %841.50 (which will give 26.67 left to add to savings) on a 5-year plan.

(I really do not understand this question because there is no specified year amount or interest rate to work from. Obviously banks won't allow a 5-year plan, but I got her monthly payment as close to $868.17 as possible with the most money borrowed to allow for the larger price she will end up paying because of the interest.)

## 30-Year Fixed Rate and Minimum Monthly Payments

Working through the Bank of America, Jenny got a 4.625% interest rate for her purchase price of $50,000 and down payment of $10,000.

Yay! Her mortgage has been approved!

With the equation 40= R((1-(1+.04625/12)^(-30x12)) / (.04625/12)), we get R = 246.29, making her minimum monthly payment, with a 30-year fixed rate, $246.29.

## Time is Money! (Save both)

Increasing her minimum monthly payment of $246.17 by 15% will make it $283.11, still very affordable for Jenny.

With the minimum payments on a 30-year fixed rate, Jenny will end up paying $88,621.20! More than double her house payment! But with the 15% increase each month, she can reduce her 30-year to a 17-year, and spend only $57,754.44 , saving $30,866.76!

We can see this with the following equation:

40,000= 283.11((1-.04625/12)^(-12X)) /(.04625/12))

141.29= ((1-.04625/12)^(-12X)) /(.04625/12))

0.545= ((1-.04625/12)^(-12X))

-0.455= (-.04625/12)^(-12X)

Log(-0.455) / Log(-0.04625/12) = -12X

[Log(-0.455) / Log(-0.04625/12] / -12 = X

X= 16.44 (rounded to 17 years)

## Citations

1)

Lower Your Spending. (2013, 12 30). *Average costs*. Retrieved from http://www.loweryourspending.com/average-cost-for-food-per-month-for-one-person.html

2)

Reece & Nichols. (2013, 12 30). *Listing search*. Retrieved from http://www.reeceandnichols.com/Listing/ListingSearch.aspx?Search=e1c7a90e-cb84-4463-91cb-ef4248430def&SearchType=&ListingType=&ListingDistrictTypeID=&FirstLetter=&Sort=6&view=

3)

Bank of America. (2013, 12 30). *Mortgage rates today*. Retrieved from https://www.bankofamerica.com/home-loans/mortgage/custom-mortgage-rates-today-results.go