# Real Life Purchase Comparisons For Prof Robert Keller LIB 112 by lonyoo

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For: Prof. Robert Keller

LIB 112: Survey of Mathematics Group Project #2 Spring 2005

By: Chris Stechman Kathleen Kraft Morgan McMeely

Real Life Purchase Comparisons General Overview: Our group was given the task of researching the various financial implications and impacts of two of life’s most common large ticket purchases: a car and a house. With both purchases we had to research the available interest rates and loan terms. Since one of the group members had just purchases a home last spring, we decided to use their actual loan amount and interest rate. This particular mortgage is based upon no down payment, a note of approximately \$55,000 over 30 years, and an interest rate of 6%. For the car we decided to do something a bit different. Instead of searching through the newspaper for a vehicle already for sale we searched the internet for a hybrid to special order. Looking over the Toyota website we found the Prius base model available for approximately \$22,500. Again we turned to the internet for further information and th is time found a note from Dupaco Community Credit Union for 60 months at 5.4%. To further examine our financial options and better understand budgeting concerns, we compared multiple repayment scenarios. On each item we examined the impact of monthly prepayments to principle and significant down payments as compared with standard monthly payments with no down payment. In all purchase scenarios, the loan amortization formula was used. This formula was actually broken down and plugged into Microsoft Excel to allow us to visualize the differences each adjustment made on the total outcome. All calculations for monthly payments were based on whole dollars even though amortization tables show accuracy to the penny.

Real Life Purchase Comparisons Address: 2511 Windsor Ave. Dubuque, IA 52001 Note Amt.: Term: Rate: Monthly Payment: Mortgage #1: \$55,000 30 years 6.0% fixed \$330

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This first example is the one used to make the actual purchase. When the decision to buy was made, other outside factors had to be considered rather than simply the long term loan costs. Since the actual monthly mortgage payment includes fees such as property tax and home owner’s insurance we had to estimate the monthly principle and interest payments. While this information could be obtained from the bank, due to time constraints the estimates of actual note value and monthly payments are accurate enough for illustration purposes. As Chart #1 shows, the loan pay off is steady and gradual. Over the life of the note approximately \$119,000 will be paid. Of this total payment, about \$63,500 will be interest. Actual calculations can be seen in Table #1. Mortgage #2: In this hypothetical situation we assumed a 20% down payment. Since all other factors remained the same, this down payment was in the amount of \$11,000. The down payment then changed the loan amount to \$44,000. With the monthly payment staying the same we were able to finish the note well ahead of time. Instead of the 360 months as established with the original example, this plan pays off the note in only 221 months. Since the amount of time was

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significantly reduced we were able to also cut total interest payments to only \$28,700. Roughly speaking, this translates to a 55% savings in interest payments with only a 20% down payment. These savings do not even take into account the reduced need for mortgage insurance and the subsequent savings there. Provided the funds are available when making the purchase, going with a 20% down payment makes the most financial sense between these two examples. Mortgage #3: In this option the assumption is a more secure financial health and better budget. Not only is the 20% down payment exercised, but an additional \$50 is applied to the principle on a monthly basis. This obviously has the shortest life and the steepest pay off curve. Since less is borrowed initially and more is applied to principle each month, less interest has a chance to accrue. The end result is the note is paid off by month 174 or only 14.5 years. That is less than half of the original note term! Over all interest payments are only \$21,900. This is only 34% of the original interest payments of our first example. Mortgage #4: This final example takes a look at a more reasonable and realistic expectation for a first time home buyer. In this example a down payment could not be afforded, but an additional \$50 per month in payments is just within reach. This compromise trims the note to only 258 months or about a 9 year savings. Total interest paid on this example is approximately \$43,000 or about 68% of original projection. Again, this is not by any means the most economical option considering it provides the least savings. However, this is the most realistic option for someone who can not afford a large down payment initially and still provides some savings over making the

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minimum monthly payments. See Charts 1 through 4 and Tables 1 through 4 for additional supporting documentation and visualization. Car: Purchase Amount: Term: Rate: Toyota Prius Hybrid \$22,500 5 years (60 months) 5.4% Since we were using the internet to check out the prices and availability of this particular vehicle, no dealer financing options were explored or available. All of our examples are based upon lowest available advertised interest rate. Car Loan #1: Again this example is used primarily as a baseline from which to compare all other car loan options. We are using the assumption of the base package vehicle at \$22,500 and securing a note as listed with Dupaco Community Credit Union at http://www.dupaco.com with a 60 month term and a 5.4% interest rate. We also chose to use Excel to help calculate the monthly payments and to chart the variations between loan scenarios. Our initial example shows a monthly payment of \$427. At this payment rate and no down payment the loan is paid off in the 60 months as prescribed. Just as discussed with the home loan purchase, this is the least economical choice long term, but allows for the quickest asset acquisition with the least amount down. Interestingly enough though, while the house loan with a longer term had a more gradual pay off curve the car is a more linear example and a steeper rate of decline. This can be inferred as being either the higher interest rate on the house or the fact the mortgage has a longer term applied.

Real Life Purchase Comparisons Car Loan #2:

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In an effort to further examine the benefits and effects of a down payment on a large ticket item, we opted to use a 20% down payment on the car. This resulted in a down payment of \$4,500 and the note for only \$18,000. All other factors remained the same to allow for better and easier comparisons. Our net effect on interest expense over the life of the note was a \$1,189 savings. Our stretching to pay the 20% down on the vehicle reduced the term from 60 months to only 47 months and we realized a 38% savings in total interest payments. Car Loan #3: Again, like we found with the house this is the most economical way to purchase any large dollar item on time. We shortened the amount of time on the note quite considerably from 60 months down to only 41 months. This is accomplished by coupling a lower initial loan amount and a faster repayment of the principle by including the bonus \$50 each month. These two simple actions reduced the entire interest expense by nearly 45%. Unfortunately as college students we would most likely not have the liquid assets readily available for the larger down payment and still be able to cover all the incidental expenses of new vehicle ownership. Sadly enough, this money saving option would not be highly advised in that particular light and so would not be practical. Car Loan #4: Much as was expected, this loan option allowed for the most likely purchase method since no down payment was required and yet we could realize some of the interest expense savings by making our additional \$50 monthly payment towards principle. Surprisingly enough though, the extra payment each month did not create as significant a savings as on the home loan. Only seven months were shaved off the term of the loan and only a 12% reduction in interest costs were

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gained. As a result of this meager savings, option #2 is much better if a down payment can be obtained. If this is a first vehicle then the monthly bonus payments may be the only option available to simply begin building assets. Conclusions: In an ideal world where additional expenses were not a concern, the wisest loan option would be to not take out a loan to begin with. Accepting the idea of a bank loan being a necessity in life the next best option is to make as large a down payment as can be afforded and to consistently make additional monthly payments directly towards principle. While time is a friend and works with you when building a savings or retirement plan, it is also the devil and can ruin you when working with any kind of debt load. To verify accuracy of our primary amortization table for each purchase we checked online with a financial calculator. Using Google search services we found our calculator at http://mortgage-x.com/calculators/amortization.htm. In the case of the home loan our calculations were actually correct when compensating for our use of whole dollars to make the monthly payment.

Real Life Purchase Comparisons Appendix 1 Internet Based Mortgage Amortization Table

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Real Life Purchase Comparisons Appendix 2 Internet Based Car Loan Amortization Tables

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Real Life Purchase Comparisons Appendix 3 Home Mortgage Charts & Tables

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Real Life Purchase Comparisons Appendix 4 Car Loan Charts and Tables

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