My Math Forum How to solve for monthly amount to get $200k payout after specific payment term?  User Name Remember Me? Password  Algebra Pre-Algebra and Basic Algebra Math Forum  February 18th, 2017, 06:45 AM #31 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Ya. Imagine trying to explain a formula involving logs and the likes! 1st thing I do when I try to solve a problem given here is change the damn given example to something as simple as possible. Like, in this case: target = 28830, r = .10, term = 27 : Code: 01 1000 1000 02 1000 2000 ... 12 1000 12000 13 1100 13100 ... 24 1100 25200 25 1210 26410 26 1210 27620 27 1210 28830 Now my formula need to yield an even 1000 bucks! Get my drift February 18th, 2017, 07:26 AM #32 Senior Member Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 Quote:  Originally Posted by Denis Ya. Imagine trying to explain a formula involving logs and the likes! 1st thing I do when I try to solve a problem given here is change the damn given example to something as simple as possible. Now my formula need to yield an even 1000 bucks! Get my drift What I actually did in my spread sheet was to work out the sum of the payments starting with an initial payment of 1 dollar (the number of years, months, indexation percentage, and total to be disbursed were input variables). Then I divided that sum into the total to be disbursed. Same idea except I started with a simple payment rather than a simple total. I think skipjack may have been there from the start, but I really did not get what the problem even was until about page 2.  February 18th, 2017, 09:50 AM #33 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Mine was using future value of annuity formula (treating the percentage increase as an interest rate) for the complete years, then adjusting by subtracting above from the target amount... as you say, same general idea... February 18th, 2017, 06:33 PM #34 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Quote:  Originally Posted by SDK Finally, if a particular value for$S$is specified one can factor and solve for$P_0$explicitly which is $$P_0 = \frac{S}{12(\frac{1-(1+r)^Y)}{r}) + M(1+r)^Y}.$$ Just noticed that +M(1+r)^Y should be -M(1+r)^Y. After that change plus inserting the missing half bracket, it works fine. Plus simpler than mine  February 18th, 2017, 07:28 PM #35 Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2205 It should be$P_0 = \dfrac{S}{12((1 + r)^Y - 1)/r + M(1 + r)^Y}$.  February 18th, 2017, 07:59 PM #36 Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Skip, doesn't that simply change the result from negative to positive? Anyway, I prefer positive! March 31st, 2017, 02:17 AM #37 Newbie Joined: Mar 2017 From: Portland, OR Posts: 5 Thanks: 0 Quote:  Originally Posted by mshaughn I am trying to find a formula to solve for the monthly starting amount below: Monthly Starting Amount = ? Payment Term = 10 years, 5 months (125 monthly payments) Indexation = 2% per year, compounded Total Future Payout = \$200,000.00 That is, what is the required monthly starting amount you must invest if you want a payout of \$200,000.00 after 125 monthly payments, if payments increase by 2% per year, compounded? I know the answer is \$1,454.63 with \$0.45 remaining at the end of the term, but I am not sure how to get there. Any help would be appreciated. I also know that without indexation, it's simply \$1,600.00 (\$200,000.00 / 125). Using the =PMT formula, I got about 1500 as payment but that's a fixed 2% APR per year (not counting it as increasing by 2% each time - i'm not sure how to enter this in excel).  March 31st, 2017, 09:56 PM #38 Senior Member Joined: May 2008 Posts: 301 Thanks: 81 Beer soaked comment follows. I must have been sober at the time when this thread started out. Good stuff.  Tags$200k, amount, monthly, payment, payout, solve, specific, term

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