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avatar+656 

soooo 1st question: 
does it matter what order the explicit formula for the arithmetic function is written in?? for example i write it as 
\(f(n)=d(n-1)+f(1)\)

let's just say \(f(1)\) is defined. 
is that right? 
                                                                                                                                                                   
and also i really dont understand this question: 
A company is offering a job with a salary of $30,000 for the first year and a 5% raise each year after that. If that 5% raise continues every year, find the total amount of money you will have earned by the end of your 5th year. 

So this is what I did, but I have gotten a different answer from what the answer key says and I don't know where I went wrong. 

\(f(1)=30,000 \)

\(f(n)=30,000(1.05)^{n-1}\)

\(\sum_{n=1}^{5} 30,000(1.05)^{n-1}\) \(\)

 

and I ended up getting $165,768.94 

does anybody know what i did wrong?? or how you solve it if that is the wrong answer. I'm really confused.
                                                                                                                                                                    

 

Thank you in advance!! 

 Sep 24, 2019
edited by Nirvana  Sep 24, 2019
 #1
avatar+6045 
+1

That's what I get.

 

What's the answer they give?

 Sep 24, 2019
 #5
avatar+656 
0

the answer they gave was $166,162.96

Nirvana  Sep 24, 2019
 #6
avatar
+1

It appears they have the 5% annual raise compounded monthly for 5 years !!!. This is the formula used to arrive at their number: FV =P{[1 + R]^N - 1/ R} =30,000 x {[1 + 0.0512]^5 - 1 / 0.0512}

FV = $30,000 x {[ 1.283591288862 - 1] / 0.0512}

FV = $30,000 x {0.283591288862 / 0.0512}

FV = $30,000 x             5.5388923606..........

FV = $166,166.77 - the small discrepancy is due to rounding off the interest rate to 2 decimal places.

Guest Sep 24, 2019
 #7
avatar+656 
0

could you explain why you got that number and how? :')
i am really confused. 

Nirvana  Sep 25, 2019
 #8
avatar
+1

They have compounded the 5% monthly, which  is done like this: [1 + 0.05/12]^12 = 1.05116189788 - 1 =5.116189788% . They seemed to have used this rate to sum up the $30,000 salary for 5 years as follows:

 

∑[30000 * 1.051188^n, n, 0, 4] =$166, 162.79

Guest Sep 25, 2019
 #9
avatar+656 
0

why is it over twelve?

Nirvana  Sep 25, 2019
 #10
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+1

Because you have 12 months in 1 year, and is compounded monthly.

Guest Sep 25, 2019
 #11
avatar+656 
0

ohhh 
but what do you mean by compound? 

Nirvana  Sep 25, 2019
edited by Nirvana  Sep 25, 2019
 #12
avatar
+2

You should study "compound interest" which is very common in financial  investments. "Compound interest" means: You earn interest on interest.

Guest Sep 25, 2019
 #13
avatar+656 
0

ahhhh i see!!! okay i understand how they got that number now :) thanks 

Nirvana  Sep 25, 2019
 #2
avatar+19822 
+1

Same here....that is the answer i got.

 Sep 24, 2019
 #3
avatar
+1

Try non-compound raise of 5% and see if that agrees with their answer! You never know what they had in mind !!

$30,000 + [$30,000 x 1.05 x (5 - 1) ] =$30,000 + $126,000 = $156,000.

It is NOT really 5% annual raise after the first year but more like 4.66% annual raise!.

 Sep 24, 2019
 #4
avatar
+1

If it is wrong maybe the question asks the money that is earned by the end of 5th year Not the sum of all the money earned from 1st year till 5th year.

so it is: 

f(5)=30000*(1.05)^4

=36,465.1875

 Sep 24, 2019

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