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Chapter 4 Loans and Finances . Gordon Chow Math 1030. The Why. Why is it important to make financial goals. You gain insight as to where your money goes You can use interest to your advantage You can suffer less from interest gaining from a loan

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## Chapter 4 Loans and Finances

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**Chapter 4Loans and Finances**Gordon Chow Math 1030**The Why**• Why is it important to make financial goals. • You gain insight as to where your money goes • You can use interest to your advantage • You can suffer less from interest gaining from a loan • You are able to know how long a payment will take to repay**What Should I Pay**• The Average percentage for living expenses should be about 1/4 of your income. • Your average payment on your car should be about a 1/3 of your income • That is 1/4 + 1/3 = 3/12 + 4/12 = 7/12 = 58.333% Goes to car and house payments.**Does Money Make You Happy**• Research has been accomplished from Princeton that states • Money does not make you happier • Because people with money have no easier time dealing with face to face situations**Does not having Money Affect you?**• Yes, • People with financial strife have higher • Divorce rates • Relationship difficulties • Higher depression Rates • And other problems**How to Come Up With a Goal**• How do you decide your goal • How much a month do you want to pay? • When do you want to pay it off? • What is the total amount you are willing to spend? • These are all things to consider**Review Savings Plan Formula**• The Savings plan formula • A=PMT[(1+r/n)nt-1)] • (r/n) • Where A=your total • PMT=Monthly payments • r=annual interest rates • n=number of compounding periods per year • t=time**Example**• We are going to buy a car • Lets just say for realisms sake I want a Ferrari Enzo roughly $1,000,000 • We want to pay $18,000 a month • Our interest rate is 3.24% compounding monthly • How long will this take to pay off?**Plug it in**• A=PMT[(1+r/n)nt -1)] • (r/n) • A=$1,000,000.00 • PMT=$18,000.00 • r=.0324(from 3.24%) • n=12(number of compounds in 1 year) • t=?**Plugged In**• $1,000,000.00=$18,000.00 [(1+.0324/12)12t -1)] • (.0324/12) • A=$1,000,000.00 • PMT=$18,000.00 • r=.0324(from 3.24%) • n=12(number of compounds in 1 year) • t=?**Plugged In**$1,000,000.00=$18,000.00 [(1+.0324/12)12t -1)] (.0324/12) Now we try to isolate the variable t $1,000,000.00=$18,000.00 [(1+.0324/12)12t -1)] .0027**Plugged In**$1,000,000.00=$18,000.00 [(1+.0324/12)12t -1)] .0027 Now multiply both sides by the denominator .0027 And we get $2,700.00=$18,000.00 [(1+.0324/12)12t -1)]**Plugged In**$2,700.00=$18,000.00 [(1+.0324/12)12t -1)] Now we divide by $18,000.00 .15= [(1+.0324/12)12t -1)] I solve for inside the parentheses .15= (1.0027)12t -1**Plugged In**.15= (1.0027)12t -1 Now add 1 1.15= (1.0027)12t Now what do we do? A variable is in the exponent. Now to learn about logs**Logs**• We know that 102=100 • What if it was a variable 10x=100 • We still know that the x=2**Rules of logs**• Well if we had a log equation such as Log101,000 (If no base is listed it is assumed 10) • This is equal to 3 • This is essentially saying to what power of 10 makes 1,000 • What about Log10100,000 • This is equal to 5**Rules of logs**• Log101,000 • This is equal to 3 • What about Log10100,000 • This is equal to 5 We can prove this because 10*10*10=1,000 And 10*10*10*10*10=100,000**Another Rule**• If you have the same subscript in a Log multiplied as the same numerator you can bring down an exponent. • Confusing I know let me show you**Examples**• Log10101=1 because Log10101 • Log14141=1 because Log14141 • Log1010X=X because Log1010X • Log1414X=X because Log1414X • Log145614561234=1234 because Log145614561234**Change of Base Formula**Most calculators don’t allow you to change the base so you can plug equations like this directly in Log1045 = 1.65 What about this equation though Log875 = ?**Change of base formula**• Log875 = ? • Well with the change of base formula we can • Here we take the Log10(Numerator) over the Log10(Subscript) • For example Log1075 Log108 This is equal to 2.076272897**Change of Base**• We can prove this works because 82.076272897 = 75**Back to the Enzo**• We left off here 1.15= (1.0027)12t With the rule of logs we learned earlier we can multiply both sides by Log1.0027 Log1.0027 *1.15= Log1.0027 *(1.0027)12t**Enzo continued**• This leaves us with • Log1.0027 1.15= 12t • Now we can use the change of base formula Log101.15 Log101.0027 This leaves us with 51.83353193**Enzo Continued**• 51.83353193 = 12t • Now we divide by 12 to isolate the variable Now T= 51.83353193 = 4.319460994 years 12**Double Check Our Work**$1,000,000.00=$18,000.00 [(1+.0324/12)12*4.3194609944 -1)] (.0324/12) $1,000,000.00=$18,000.00 [(1.0027)12*4.3194609944 -1)] (.0027) $1,000,000.00=$18,000.00 [(1.0027)51.83353193 -1)] (.0027) Insert the value of time Solving inside the parentheses The value after multiplying**Double Check Our Work**$1,000,000.00=$18,000.00 [(1.15-1)] (.0027) $1,000,000.00=$18,000.00 [(.15)] (.0027) The value after distributing the exponent The value after you take away 1**Double Check Our Work**$1,000,000.00=$18,000.00 [(.15)] (.0027) $1,000,000.00=2,700.00 (.0027) $1,000,000.00= $1,000,000.00 The value after multiplying The Equations equal each other**Enzo**• So after over 4.3 years at $18,000 payments a month With a little over 3% interest compounding monthly I will have an Enzo**Score**("1024x768 Ferrari Enzo desktop wallpapers and stock photos")**Biblography**Works Citied Bennett, Jeffery. Using & Understanding Mathmatics A Quantitvive Reasoning Approach.. 5th edd. Lifland et al. Bookmakers, 2011. Print. Paul, Allen. ... That is the Question Critical thinking about the Human Condition. 5th edd. Custom Publisihing: Custom, 2009. Print. "princeton.edu." www.princeton.edu. princeton, 06292006. Web. 25 Apr 2011. <http://www.princeton.edu/main/news/archive/S15/15/09S18/index.xml?section=topstories>. Volivaka, Moli. Intervew by Gordon. Print. 27 Apr 2011. "1024x768 Ferrari Enzo desktop wallpapers and stock photos." http://wallpaperstock.net/ferrari-enzo_wallpapers_396_1024x768_1.html. Web. 27 Apr 2011.

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