My Math Forum Li'l annuity escapade!

 Economics Economics Forum - Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance

 July 13th, 2016, 10:34 AM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Li'l annuity escapade! Devised by yours truly, for your enjoyment! 12 annual payments of same amount are deposited (at year-end) 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: 965 Thanks: 342$1229.50 ?
 July 14th, 2016, 12:08 AM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 No.
 July 14th, 2016, 05:22 AM #4 Senior Member   Joined: Apr 2014 From: UK Posts: 965 Thanks: 342 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

Posts: 14,597
Thanks: 1039

Quote:
 Originally Posted by weirddave At the end of year one, is the amount in the account equal to the deposit amount?
Yes, of course...A = deposit amount:

0 : .00
1 : A
2 : A + 1.06A

 July 14th, 2016, 10:28 AM #6 Senior Member   Joined: May 2008 Posts: 301 Thanks: 81 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)^3-1]/.12+R*[(1.10)^3-1]/.10*(1.12)^3+R*[[1.08]^3-1]/.08*(1.10)^3*(1.12)^3+R*[(1.06)^3-1]/.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: 14,597 Thanks: 1039 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: 965 Thanks: 342 \$1389.23
 July 15th, 2016, 04:55 AM #9 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 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: 301
Thanks: 81

Beer soaked ramblings follow.
Quote:
 Originally Posted by Denis Did you hear Dexter groan?
I wish I did.
I do miss him and his coke soaked rants a lot.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Yume Economics 1 May 4th, 2015 09:34 PM Surfboard Economics 8 March 7th, 2015 09:45 AM fatim Economics 6 November 30th, 2014 07:20 PM simplequestion Economics 3 October 8th, 2008 12:41 PM Bom55 Calculus 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top