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!!

Nirvana Sep 24, 2019

#1

#6**+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

#8**+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