Question

A job pays a salary of $17,000 the first year. During the next 23 years the salary increases by 7 percent each year. What is the lifetime salary over the 24 year period?

Answer 1

\(\huge\color{pink}{WELCOME~TO~OPENSTUDY!!!}\)

Answer 2

Since the job starts of at 17,000 times 7% and the i think you would multiply by 24 i am not sure of this though @Nnesha

Answer 3

Use compounding formula

Answer 4

Regular Compound Interest Formula

P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year

Answer 5

put in this form

Answer 6

We start of with 17,000
and then each year its increased by 7%
And we would like to determine the salary in 24 years time
The formula is as follows
\[FV=P(1+r)^n\]
FV= Future Value
P=Principal Amount ... the amount we are starting off with
r- interest rate
n=number of years
So interest rate is 7% which is .07
n=24 since we wanna see what the salary will be in 24 years
P= is the amount we start off with which is 17,000

Using this info solve for FV

Answer 7

@wahahaha , you are correct but they want the total amount earned in 24 year career
use the sum formula for geometric series
\[Sum = P \frac{r^n - 1}{r-1}\]

Answer 8

Ohhh lifetime salary ,,,, didnt notice that Thanks

Answer 9

** sorry my "r" is actually "1+r" if r = int rate

Answer 10

let us not get too fancy now. I think the person doesn't even know the symbol for summation

Answer 11

haha yeah @tlaing50 , anything making sense??

Answer 12

I am not sure . I have such a hard time with these types of problems. I am completeing my last algebra class and if I can figure this one out, I will be thru and going on to Chemistry.

Answer 13

Are you familiar with summations?

Answer 14

the salaries form a geometric series:
initial value = 17000
common ratio = 1+int rate = 1.07

you need to find the sum of the series
reference:

https://en.wikipedia.org/wiki/Geometric_series#Sum

Answer 15

Not really. I am a 65 year old great grandmother who going for a degree in Human services. I have never had an algebra class until I decided to go to college. I am not doing to bad, but like I said , I amnot so good at this.

Answer 16

wait 65 great grandmother .... hmmm ok thats possible lol

Answer 17

pooja's formula will suffice and yield just the same answer

year | amount
1 17,000
2 17,000 + (17,000 * 0.07)
3 {[(17,000 + (17,000 * 0.07)] + [(17,000 + (17,000 * 0.07)] * 0.07}
etc.

Answer 18

you may be the oldest person to be on openstudy :)

Answer 19

the purpose of using the formula is so that you don't have to solve it so tediously

Answer 20

So wait you need to understand the concept or do you just just want the answer?

Answer 21

I came up with 86,230. I don't think it is right.

Answer 22

no use sum formula, not compound interest formula

Answer 23

I need the concept . Just getting answer wont help me know what I am doing.

Answer 24

Okk well let me explain the tedious way first
So basically we are adding up her salary for the next 24 years

So year #1 she had a salary of 17,000

Year #2 her salary increased by 7% so her salary in year #2 is
FV=17,000(1+.07)^1=17,000(1.07)=18,190

Year #3 her salary increased another 7% so her salary that year was
FV=17,000(1+.07)^2=19463.30

Ok we continue this for the next 22 years until we hit the 24th year

And then we add them all up
So it would be 17,000+18190+19463.30+ ......

Answer 25

you can still use the compounding formula, but you will have to adjust it since the interest is annually

Answer 26

you're just doing a succession of summation

Answer 27

if u start with Salary = S

and you get 7% more next, that is a factor increase of 1.07

so you get
S*1.07 ---> 1st year
then what you get that 1st year is again increased by a factor of 1.07
S*1.07*1.07--->2nd year
S*1.07*1.07*1.07--->3rd year
and so on
S(1.07)^n---->nth year

Answer 28

because you're doing an interest of the previous amount, which will be the Principal amount
and after a year, the the principal is the previous year's

Answer 29

just note 1st year here is taken to be the 1st year of increase
so its really the 2nd year in the grand scheme of things that you are seeing that increase of salary

Answer 30

that's why we have it as \(P(\huge 1 \large + r/n ...) \)

Answer 31

S---->1st year
S*1.07---->2nd year
S*(1.07)^2---->3rd year
.
.
.
\[S*(1.07)^{(n-1)}-----> nth~~year\]

Answer 32

Thank all of you so much, but my test just timed out , so I guess I wont get that problem right. I do appriciate all the help offered. I have written everything down, so I can continue working on the problem, just to see if I can get it right or at least know how to work these kind of problems. Again thank all of you so much.

Answer 33

because the increase starts at the indicated nth year

Answer 34

good job for keeping at it +1

Answer 35

the sum formula is just the same as the compounding formula. it gets tweaked depending on the type of compounding and APR or APY

Answer 36

Ummm just if you wanted to check yourself the answer wld be $908,414.40

Answer 37

Thank you. I am so wrong on my figures.