Kenneth recentley started a new job. his starting gross monthly salary was 3200. Each year on the anniversary of his starting date, kenneth is promised a 7% raise.
If keneth works for 5 years what was his gross annual income in his fifth year of work?
my work:
A=p(1+ i)^n
A=?
p= $3200
i: 7%
n= 5
A=p(1+ i)^n
A=3200(1+0.07)^5
a= 3200(1.07)^5
A= 4488.17 I rounded it! is this correct?
there is part b to this question!
what is the minuim number of years Kenneth will have to work to earn a gross annual income of at least $60000?
I would think I would use the same formula right?
A=p(1+ i)^n
A= $60 000
p= $3200
i: 7%
n= ?
60 000 =3200(1+0.07)^n
but I get lost here how would I get n by itself?
thanks for your help!
7% rate,3 years $21
To find the gross annual income in Kenneth's fifth year of work, you correctly used the formula A = p(1 + i)^n.
A = 3200(1 + 0.07)^5 = 3200(1.07)^5 ≈ 4488.17
So, the annual gross income in Kenneth's fifth year of work would be approximately $4,488.17.
Now, moving on to part b, to find the minimum number of years Kenneth will have to work to earn a gross annual income of at least $60,000, we can rearrange the formula to solve for n.
Starting with:
60,000 = 3200(1 + 0.07)^n
Divide both sides of the equation by 3200:
60,000 / 3200 = (1.07)^n
Simplify the left side:
18.75 = (1.07)^n
To isolate n, take the logarithm of both sides using the base 1.07 (since it's the base in the equation):
log(18.75) = log((1.07)^n)
Using the logarithm property log(a^b) = b * log(a):
log(18.75) = n * log(1.07)
Now, divide both sides by log(1.07):
n = log(18.75) / log(1.07)
Using a calculator or computer program to evaluate this expression:
n ≈ 23.02
So, Kenneth will need to work for at least 23 years to earn a gross annual income of at least $60,000.