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July 13th, 2016, 10:34 AM  #1 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,752 Thanks: 604  Li'l annuity escapade!
Devised by yours truly, for your enjoyment! 12 annual payments of same amount are deposited (at yearend) in an account, resulting in $30,000 at end of 12th year. 4 different annual interest rates are used, as following: years 1 to 3: 6% years 4 to 6: 8% years 7 to 9: 10% years 10 to 12: 12% Calculate the payment amount. 
July 13th, 2016, 11:44 PM  #2 
Senior Member Joined: Apr 2014 From: UK Posts: 710 Thanks: 271 
$1229.50 ?

July 14th, 2016, 12:08 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,752 Thanks: 604 
No.

July 14th, 2016, 05:22 AM  #4 
Senior Member Joined: Apr 2014 From: UK Posts: 710 Thanks: 271 
At the end of year one, is the amount in the account equal to the deposit amount?

July 14th, 2016, 08:16 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,752 Thanks: 604  
July 14th, 2016, 10:28 AM  #6 
Senior Member Joined: May 2008 Posts: 175 Thanks: 34  Beer soaked ramblings follow. Didn't need a beer to solve your li'l annuity escapade Sir D; but old habits die hard, two beer bottles is always better than one, so What is R in R*[(1.12)^31]/.12+R*[(1.10)^31]/.10*(1.12)^3+R*[[1.08]^31]/.08*(1.10)^3*(1.12)^3+R*[(1.06)^31]/.06*[1.08]^3*(1.10)^3*(1.12)^3=30,000 Last edited by jonah; July 14th, 2016 at 10:35 AM. 
July 14th, 2016, 11:02 AM  #7 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,752 Thanks: 604 
Looks good Sir J! My approach: R1 = .06 : a = (1 + R1)^3 R2 = .08 : b = (1 + R2)^3 R3 = .10 : c = (1 + R3)^3 R4 = .12 : d = (1 + R4)^3 u = (a  1)*b*c*d / R1 v = (b  1)*c*d / R2 w = (c  1)*d / R3 x = (d  1) / R4 P = annual payment P = 30000 / (u + v + w + x) HINT: P = ?,???.2318793... Did you hear Dexter groan? 
July 14th, 2016, 11:07 PM  #8 
Senior Member Joined: Apr 2014 From: UK Posts: 710 Thanks: 271 
$1389.23

July 15th, 2016, 04:55 AM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 8,752 Thanks: 604 
Yepper Dave. Partly illustrated: Code: YEAR PAYMENT INTEREST BALANCE RATE 0 .00 1 1,389.23 .00 1,389.23 2 1,389.23 83.35 2,861.81 6% 3 1,389.23 171.71 4,622.75 6% 4 1,389.23 353.82 6,165.80 8% .... 12 1,389.23 3,065.44 30,000.00 12% 
July 15th, 2016, 08:43 AM  #10 
Senior Member Joined: May 2008 Posts: 175 Thanks: 34  

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