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-   -   Li'l annuity escapade! (http://mymathforum.com/economics/333896-lil-annuity-escapade.html)

Denis July 13th, 2016 10:34 AM

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.

weirddave July 13th, 2016 11:44 PM

$1229.50 ?

Denis July 14th, 2016 12:08 AM

No.

weirddave July 14th, 2016 05:22 AM

At the end of year one, is the amount in the account equal to the deposit amount?

Denis July 14th, 2016 08:16 AM

Quote:

Originally Posted by weirddave (Post 542508)
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

jonah July 14th, 2016 10:28 AM

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

Denis July 14th, 2016 11:02 AM

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? :)

weirddave July 14th, 2016 11:07 PM

$1389.23

Denis July 15th, 2016 04:55 AM

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%


jonah July 15th, 2016 08:43 AM

Beer soaked ramblings follow.
Quote:

Originally Posted by Denis (Post 54253)
Did you hear Dexter groan? :)

I wish I did.
I do miss him and his coke soaked rants a lot.


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