~TLDR at the bottom~
1. The problem statement, all variables and given/known data
The Big question:
Suppose you can put $250/month into a retirement account that pays a 6% (annualized) return on investment.
When you reach 65 years of age, how much will you have in your retirement account? [“Annualized” refers to “on a yearly basis”
—this is why you see things like “i/12” in formulas (or “i/n” in general). 6% annually would correspond to 6%/12 = 0.5% per month.]
At this point when you retire, you move your money into a lowrisk account that pays 3% (annualized) return on investment.
If you plan to live for 15 more years, how much can you draw out each month to live on?

Variables Account 1:
Variables Account 2:
A_{1}=155123.83
R=.0025
N=12
T=15
2. Relevant equations
Annuity Formula(Given):
A=P[(1+(r/n))^{nt})1]
______________
(r/n)
3. The attempt at a solution
For the savings account it was easy.
My Attempt:
A=250((1+(.005/12))^((12)(46))1)/(.005/12)
A=$155123.83
(This answer was received using my age of 19)
After this point it shows my attempts at solving the second part of the question.
If you know how to solve it skip this next very long and very tedious section.
If you are trying to solve it and am not sure how,
the next part may inspire you or just confuse you.
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The second part is tricky. I must find the compound interest while removing money.
My First Attempt:
Solve for P using annuity
Variables:
A=155123.83
R=.0025
T=15
N=12
Formula:
155123.83=P[(1+(.0025/12))^((12)(15))1]
______________
(.0025/12)
P=$12912.18
This cannot be true if A is the annuity than P would be what you add per month to get A.
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My Seccond Attempt:
Sum of a Geometric Sequence
Variables:
A_{1}=155123.83
R=1.0025
N=180
Formula:
((155123.83)(11.0025^180))
____________________
(11.0025)
I felt this would give me the end amount but without the money removed each month which is unhelpful :(.
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My Third Attempt:
Indicated Sum
Variables:
X=180
I=155123.83
F=(ix)(11.0025^180))/(11.0025)
Assuming:
X
[itex]\Sigma[/itex] F
I
Formula:
180
Ʃ (ix)(1.0025)
155123.83
Which i see no way i would be abel to solve for x this was also a dead end :(
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My Final Attempt:
Recursion
Variables:
A_{1}=155123.83
A_{N}=A_{n1}x)(1.0025)
N>=180
Formula:
A_{N}=A_{n1}x)(1.0025)
A_{1}=155123.83
A_{2}=(155123.83x)(*1.0025)
But as you see i cannot solve for x without knowing what A
_{180} equals. and i cannot find what A
_{180}
equals without X.
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I'm sure there is a way to do it that i am just missing. As you can see i did try....
I do not necessarily need the answer just a push in the right direction.
And if you get the answer show your work so i do not lose my mind wondering.
_______________________________________________________________________ ____
TLDR: Answer the problem and show work ;)
TLDR EXTENDED:
$250/month into a retirement account that pays a
6% (annualized) return on investment.
When I am 65 the amount in the account will be A.
A=$155123.83

you put the money from the first account into another account. this account pays a
3% (annualized) return on investment. At age 65 If you plan to live for 15 more years,
how much can you draw out each month to live on?
