Sequence and Series Real Life Applications

Salary Increase

• A salary increase is different for all jobs. In this particular case we had a software engineer who made 140k. Since his salary increases by 5% a year, we have to use geometric formulas to solve.
• Salary Increase: y= 0.05s
• y= salary increase for that year
• s= salary of previous year
• This looks more familiar when seen as a recursive formula
• r= 0.05
• An-1= previous salary
• After calculating An it has to be added back to An-1, so that the salary for the new year can be found.

Cont.

• This can also be calculated using the explicit formula, which does not require knowing the previous years salary.
• a1= 140,000
• r= 0.05
• n= number of years
• The summation of geometric series can be used to find the total money made.
• a1= 140,000
• r= 0.05
• n= years passed

Depreciation of a Car and Car Loan (cont.)

Citations

Cont.

Savings Account

http://www.newhorizonsmath.com/3/post/2011/11/explicit-vs-recursive-formulas-for-arithmetic-sequences.html

http://www.regentsprep.org/regents/math/algtrig/ATP2/ArithSeq.htm

http://worldcarslist.com/images/ferrari/ferrari-599-gtb/ferrari-599-gtb-04.jpg

http://static.ddmcdn.com/gif/need-bank-account-1.jpg

http://www.worldcarwallpaper.com/the-2013-ferrari-f150-cars-hd-wallpaper/

• The software engineer in our example puts $14,000 into his savings account, which is $1166.67 a month. He already has put $1000 in it.
• The compounded annually formula can be used to solve this.
• This is quite similar to:
• a1= 1000
• r= 0.05
• n= 1

• The recursive formula can be used as well
• r= 0.05
• An-1= previous amount in account
• The summation of finite geometric series can be used to find how much money will be in the account from interest.
• a1= $1000
• r= 0.05
• n= number of years

• The recursive formula can be used:
• an-1=The previous amount
• d=$45,000.00
• The summation of arithmetic sequences can be used to find how long it will take to pay off the car loan.
• n=5
• a1=$45,000.00
• an=$225,000.00

Depreciation of a Car and Car Loan

• Depreciation of a car can be found using an arithmetic sequence.
• The loss of value of the Ferrari can be found using the equation:
• y= 500+750z+0.10x
• x= miles driven
• z= years old
• The explicit formula can be used:
• d= $0.10
• n=How many miles that have been driven
• A1= First mile = $0.10
• The recursive formula can be used as well:
• d= $750.00
• an-1= the previous term of money lost
• For example: If the car is 2 years old, then one year is 750, and I want to find how much the car lost in the second year,
• An= 2nd year
• An-1= 1st year = 750
• An-1+D = 750+750 = How much the car lost in value over 2 years.

Cont.

• In order to find the amount needed for the payoff, you need to add all of the terms of the explicit and recursive formula and then add the constant and subtract from the original price of the car.

Situation

There is a software engineer that has a salary of 140k a year. He receives a 5% salary increase per year. He buys a Ferrari 599 GTB, which costs 550k and loses 10 cents for every mile you drive. Every year the cars value goes down by $750.00 and it lost $500.00 in it's value, as soon as it was driven off the lot. Also, the software engineer has to pay off the car loan for his Ferrari. He pays a monthly installment of $3750 on his car. Lastly, he has a savings account, which compounds yearly at 5% and he puts in $1166.67 every month into this account.

Sequence and Series Real Life Applications