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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.