FINITE MATH 100% ORIGINAL & A+ QUALITY WORK
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week4.pptxHousing Market State College, PA
Average home price is $135,000
Nice Starter Home
Good Community
James Franklin comes over for the kids birthday parties
Can see Beaver Stadium from porch
State College is the best place to live. Well at least it was until the Jerry Sandusky scandal. Anyway we like to pretend that never happened around here. The new head coach, James Franklin, who is way better than Bill Obrien is a football god. Go lions!
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Mortgage rate and terms
Local PNC branch got us approved and gave us candy!
3 year term
6.1% compounded monthly
$135,000 beginning balance
A buyer’s manta should be to purchase a home that is financially comfortable.
Do your research in finding financial assistance to seek out good interest rates.
In looking for financing, there are various rules of thumb that will help you get an idea of how much home you can afford. We chose a short term, 3years, because we want to reduce the total interest paid in. Most people take home loans out for 30 years!
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Objectives
Reduce total interest, hence the short term
Get payment below $3,500 a month
Find ideal down payment that reduces interest, fits comfortable payment range, but doesn’t break the bank.
If you're using FHA financing, your home payment can't exceed 31 percent of your monthly income. But, with some mitigating factors, FHA will let you go higher.
For conventional loans, a safe formula is that home expenses should not exceed 28 percent of your gross monthly income.
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Mathematical Model
The average cost of a new home in State College, PA is 135,000.
With our decent credit score PNC Bank would approve us for a 3-year mortgage at 6.1% compounded monthly. However in an attempt to reduce total interest paid we will calculate assuming; no money down, $10,000 down and, $25,000 down.
We will construct a spread sheet in excel which will show remaining balance per year, total interest paid for each scenario assuming all payments made on time, and payment. Then to find balance per year will we change n accordingly in our excel model.
A continuous repayment is a mortgage loan which is paid by way of a continuous annuity. Generally, settling of mortgages occur over a period of years by a series of annuities with each payment accumulating compound interest from the time the deposit is made till the end of the mortgage life. Present value equations were used to determine the monthly payments for each case.
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Calculation
Payment and balance are found from the present value equation;
PV=PMT(
Where PV is present value, PMT is payment, i is rate, and n is number of periods.
N=36, i=0.061, starting PV=135,000
Interest is found using; Interest paid = (i/12)balance.
For the first payment when balance is the full 135,000
interest paid on the first payment= (0.061/12)135,000 = $686.25.
This reflects the highest single interest payment as interest is largely collected in the beginning of a loan, down payments make a big difference. Also not that the interest payment shown above represents the case with a zero down payment.
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Zero Down
Payment = $4,113.08
Total interest paid over course of the loan assuming all payments made on time is $13,070.92
Both interest paid and monthly payment are higher than we would like.
As stated in the objectives we seek a payment that is below $3,500 and with zero down the payment is way out of our price range. The above graph appears nearly linear but really the slope increases as the x axis moves to the right. In the latter months more of the monthly payment goes directly to the principle and is not lost to interest. At the end of every month we will be making a constant payment of $4,113.08 to PNC Bank of which a part will be principal and the rest interest. Interest will be reducing by the expiry of the loan term because at any one time the outstanding principal is being offset
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Principle Balance
135000 131573.16879400707 128128.91786271702 124667.15865585957 121187.80217303394 117690.75896142061 114175.93911348158 110643.25226464887 107092.60759100124 103523.91380692925 99937.079162788228 96332.011442539486 92708.617961379467 89066.805563356887 85406.480618977701 81727.549022797917 78029.916191004217 74313.487058982239 70578.166078872484 66823.857217113837 63050.463951974576 59257.889271070861 55446.035668872551 51614.805144196398 47764.099197686475 43893.818829281794 40003.864535671055 36094.136307734458 32164.53362797252 28214.955467921791 24245.30028555747 20255.466022682798 16245.350102305181 12214.849425998978 8163.8603712548847 4092.2787888158423 -5.9844751376658678E-10Month
$10,000 Down
Payment = $3,808.41
Total Interest = $12,102.71
Payment still a little high
Putting $10,000 down saves us nearly $1000 dollars over the course of the 3 year mortgage.
With $10,000 we get closer to our desired payment but it is still a little high. The above graph helps to show how mortgage lenders collect interest. It is clear that the slope is greater during the early life of the mortgage and slowly reduced in the later months. Since interest is largely collected early it a down payment has a large impact on reducing total interest paid. Here we are able to recover nearly 10% of down payment in interest savings.
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Interest
635.41666666666663 1254.7039580582123 1857.7798831836551 2444.5620342644756 3014.9675846159471 3568.9132865176953 4106.3154690734345 4627.0900360598216 5131.1524637643797 5618.4177988124266 6088.8006559829573 6542.2152160134283 6978.5752233933781 7397.7939841468324 7799.7843636034404 8184.4587841582761 8551.7292230202565 8901.5072099491081 9233.7038249808375 9548.2296961416359 9844.9949971501574 10123.909445108129 10384.882298179211 10627.822353256061 10852.637943615542 11059.236936562007 11247.526731058606 11417.414255346554 11568.805964552288 11701.607838282476 11815.725378206782 11911.06360562836 11987.527059041988 12045.019791679792 12083.445369044495 12102.706866430126
$25,000 down
Payment = $3,351.40
Interest $10,650.38
We say nearly an additional $1500 by upping money down from $10,000 to $25,000 and payment is below the desired $3,500
Again notice the same trend line as before. We save $2420.54 in interest by putting $25,000 down compared to not putting any money down. The payment is below our budget constraint. See how the slope slowly decrease from a maximum at month one and a minimum, zero slope, at month 36. Nearly all of the payments go towards principle near the end of the term. Our model doesn’t account for paying over the required monthly payment but that is another great way to reduce interest.
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Interest
559.16666666666663 1104.1394830912268 1634.8462972016164 2151.2145901527383 2653.1714744620331 3140.6436921355717 3613.5576127846221 4071.8392317326429 4515.4141681126539 4944.2076629549347 5358.1445772650022 5757.1493900918167 6141.1461965861727 6510.0587060492126 6863.8102399710278 7202.3237300592837 7525.5217162578256 7833.3263447552144 8125.6593659831369 8402.4421326046395 8663.5955974921399 8909.0403116951547 9138.6964223977066 9352.4836708653347 9550.3213903816777 9732.1285041745668 9897.8235233315754 10047.324544704969 10180.549248806015 10297.414897688581 10397.83833282197 10481.735972952958 10549.023811956951 10599.617416678218 10633.431924759157 10650.382042458512
Conclusion
We are going to put the full $25,000 down
This saves us $2,420.54 dollars in interest compared zero down
We wanted our payments below $3,500 and they are $3,351.40
Most interest is paid in the beginning, this is obvious because interest is a function of balance and balance is highest in the beginning. So by putting money down total interest is greatly reduced. In our case we recover nearly 10% of our payment in interest savings.
We like to consider ourselves to be financially responsible people and we hope that we better prepared you for your future financial planning. Thank you.
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Work Cited Page
Barnett, R. A., Ziegler, M. R., and Byleen, K. E. 2011)
Finite Mathematics for Business, Economics, Life
Sciences, and Social Sciences (12th ed.)
Retrieved from the University of Phoenix eBook
Collection database.
Dratch, D. 6 must –do before buying a home.
Retrieved from
http://bankrate.com/finance/mortgages/6-
must-d0s-before-buying-a-home-3.aspx
www.oxforddictionaries.com/definition/english/formula
