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September 27th, 2017, 04:49 AM  #1 
Senior Member Joined: Aug 2014 From: Mars Posts: 100 Thanks: 9  Financial math,
I need to make 2000$ per month in retirement when I retire at the age of 70. I need to place enough savings into an account earning 5% compounding weekly. If I start saving when I'm 41 into an ordinary earnings account earning 7%. Then what do my monthly payments need to be to make this happen? I know the Ordinary Annuities equation and the Annuities Due equation, but I can get this one. I feel like there's simple algebra that needs applying, but I can't see it. I need the equation. You don't have to solve the problem for me. 
September 27th, 2017, 08:26 AM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,688 Thanks: 701  Quote:
For how long will the 2000 be for? Life? If for life, then the monthly interest amount must equal 2000, so: "value of account at age 70" * rate/12 = 2000. Assumes the rate is monthly compounding. CLARIFY the rates: the 5% cpd. weekly is WHEN? Before or after retirement? the compounding frequency of the 7% is WHAT?  
September 28th, 2017, 04:10 AM  #3 
Senior Member Joined: Aug 2014 From: Mars Posts: 100 Thanks: 9 
I get it. I don't know how to ask the question. This next question near verbatim, with names and numbers, changed. "Bob needs 2000 dollars a month for living expenses when he retires at the age of 70. He wants to have enough money when he retires so that he will earn 200 dollars a month in interest each month if all of his savings are placed in an account earning 5% compounded weekly. If he starts his savings when he is 41 years old by making equal payments every month into an ordinary annuity earning 7%, how big do those payments have to be to generate enough money for him to live off of the interest each month when he retires?" ALthough I need the formula, it has occurred to me that I don't know how to parse out the odd wording of weeks being converted to months. And if this paragraph makes no sense, please focus on the middle one. I don't know how to ask this question. 
September 28th, 2017, 04:59 AM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,688 Thanks: 701  Quote:
Is the 7% also cpd. weekly? I assume you mean: equal payments made from age 41 to age 69, so for 29 years. AND why are you not using monthly cpd. interest? Weekly is ok, BUT why complicate! Last edited by Denis; September 28th, 2017 at 05:02 AM.  
September 28th, 2017, 06:24 AM  #5  
Senior Member Joined: Aug 2014 From: Mars Posts: 100 Thanks: 9  Quote:
 
September 28th, 2017, 07:19 AM  #6 
Senior Member Joined: May 2016 From: USA Posts: 803 Thanks: 319 
Yes, algebra is the answer, but the problem is BADLY formulated as denis has said. I am going to assume the following: Bob is investing at the start of each month into a fund that pays at a 7% annual rate compounded monthly. (The problem does not say whether the money is invested at the start or the end of the month. It does not say whether the 7% is daily, weekly, monthly, annually. It does not say whether it is a rate or a yield. It does not say what the compounding period is. Incredibly sloppy.) Bob will be investing in an account that pays at a 5% annual rate compounded weekly. (The problem does not say whether the 7% is daily, weekly, monthly, annually. It does not say whether it is a rate or a yield. Again, incredibly sloppy.) And Bob wants his $2000 per month to come from interest only without touching principal at the start of each month. (The problem does not say that withdrawals are to occur at the start of the month or the end of the month and whether they are to come only from interest earned or not because this teacher is a complete clown.) I am also going to assume that the year contains exactly 52 weeks because this is happening in a parallel universe. Under those assumptions: Bob must invest a at the start of each month for b months. The investment will earn interest at a 7% annual rate compounded monthly. At the end of b months, he will receive a lump sum c. He retains d to live on for the next 4 weeks, invests e into an account earning interest at a 5% annual rate compounded weekly, and withdraws d at the end of every two weeks. First problem to solve: what is d if Bob will have 2000 in an average month? Second problem to solve: what then is e? Third problem to solve: so what is c? Fourth problem to solve: consequently what is b? Fifth and final problem to solve: what is a? 
September 28th, 2017, 09:03 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,688 Thanks: 701 
Turns out relatively simple(?): Step1: convert 5% weekly to monthly equivalent: r = (1 + .05/52)^52  1 = .0512458 Step2: calculate required amount after 348 months (age 41 to 69) that will earn 2000 dollars monthly using (r/12)%: f = 2000 / (r/12) = 468331 (rounded to closest dollar) Step3: calculate monthly deposit in 7% cpd. monthly account that will accumulate to 468331 after 348 months: n = 348 i = .07/12 f = 468331 d = monthly deposit = ? d = f*i / [(1 + i)^n  1] = 415.86 Over and out!! 

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