SOLUTION: Heather is planning to invest a constant amount of money at the end of every year for 15 years and then allow her money to accumulate interest for 15 more years without any additio

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Question 1116001: Heather is planning to invest a constant amount of money at the end of every year for 15 years and then allow her money to accumulate interest for 15 more years without any additional deposits. If her investments earn 11% compounded annually and she must have $650,000 in 30 years, how much will she invest at the end of each of the next 15 years?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I will solve the problem in two steps.


Step 1.  Determine how much money  "X"  Heather must have in her account at the end of the first  15-years period to get  $650,000
             at the end of the 30 years period ? 

At this time interval, from 16-th year to 30-th year inclusively, the amount grows as an geometric progression with the common ratio of (1+0.11) = 1.11,

so this formula works at this time interval


    X%2A1.11%5E15 = 650000,   which gives  X = 650000%2F1.11%5E15 = $135852.83.


Step 2.  Determine a constant amount of money "Y" Heather must invest in her account at the end of each year
             of the first 15-years period to get  $135852.83  at the end of this period ? 

At this time interval, from the 1-th year to 15-th year, the amount grows/accumulates as ORDINARY ANNUITY SAVING PLAN according the formula


    Y%2A%28%281%2B0.11%29%5E15-1%29%2F0.11%29 = 135852.83,   which gives  

    Y*34.40536 = 135852.83,  and then   Y = 135852.83%2F34.405356 = $3948.59.


Answer. The amount under the question is $3948.59.

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On geometric progressions,  see the introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

On Ordinary Annuity saving plan see the lesson
    - Ordinary Annuity saving plans and geometric progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.