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July 13th, 2016, 10:34 AM   #1
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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.
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July 13th, 2016, 11:44 PM   #2
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$1229.50 ?
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July 14th, 2016, 12:08 AM   #3
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No.
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July 14th, 2016, 05:22 AM   #4
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At the end of year one, is the amount in the account equal to the deposit amount?
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July 14th, 2016, 08:16 AM   #5
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Quote:
Originally Posted by weirddave View Post
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
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July 14th, 2016, 10:28 AM   #6
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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.
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July 14th, 2016, 11:02 AM   #7
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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?
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July 14th, 2016, 11:07 PM   #8
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$1389.23
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July 15th, 2016, 04:55 AM   #9
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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%
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July 15th, 2016, 08:43 AM   #10
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Beer soaked ramblings follow.
Quote:
Originally Posted by Denis View Post
Did you hear Dexter groan?
I wish I did.
I do miss him and his coke soaked rants a lot.
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