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June 20th, 2013, 07:44 PM   #1
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Need Help with Accumulated Value

Hi Guys,

I'm new here.
I have a problem with an exercise equation which I don't understand.
Please have a look at the image:

[attachment=0:27uqbqpq]2013-06-21_101901.gif[/attachment:27uqbqpq]

My question is:

1. I don't think the line 2 is correct, why the 100 are subsctracted and still in the row
2. Where does line 3 coming from??
Attached Images 2013-06-21_101901.gif (23.7 KB, 898 views) June 21st, 2013, 12:34 PM #2 Global Moderator   Joined: May 2007 Posts: 6,823 Thanks: 723 Re: Need Help with Accumulated Value To get from line 1 to line 2, factor out 100(1+i)^4. Line 2 has an error in that all the other 100's shouldn't be there. It looks like a typo. Take them all out and you go from line 2 to line 3 using the standard formula for geometric progression. June 21st, 2013, 07:39 PM #3 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: Need Help with Accumulated Value I assume you're solving for i. Why insert the "100"s in there?! Take 'em out! AND, shortening further: let u = 1+i u^4 + u^8 + .... + u^40 = 5(u^4 + u^8 + .... + u^20) : see how unwieldy that is? Using geometric series formula: (u^44 - u^4) / (u^4 - 1) = 5[(u^24 - u^4) / (u^4 - 1) Now doing the math: u^44 - u^4 = 5(u^24 - u^4) u^4(u^40 - 1) = 5[u^4(u^20 - 1)] (u^40 - 1) / (u^20 - 1) = 5 (u^20 - 1)(u^20 + 1) / (u^20 - 1) = 5 u^20 + 1 = 5 u^20 = 4 u = 4^(1/20) = 1.071773.... So i = .071773.... June 21st, 2013, 07:44 PM   #4
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Re: Need Help with Accumulated Value

Quote:
 Originally Posted by Denis I assume you're solving for i. Why insert the "100"s in there?! Take 'em out! AND, shortening further: let u = 1+i u^4 + u^8 + .... + u^40 = 5(u^4 + u^8 + .... + u^20) : see how unwieldy that is? Using geometric series formula: (u^44 - u^4) / (u^4 - 1) = 5[(u^24 - u^4) / (u^4 - 1) Now doing the math: u^44 - u^4 = 5(u^24 - u^4) u^4(u^40 - 1) = 5[u^4(u^20 - 1)] (u^40 - 1) / (u^20 - 1) = 5 (u^20 - 1)(u^20 + 1) / (u^20 - 1) = 5 u^20 + 1 = 5 u^20 = 4 u = 4^(1/20) = 1.071773.... So i = .071773.... ~7.18% cpd annually, I'll bet  June 21st, 2013, 07:57 PM   #5
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Re: Need Help with Accumulated Value

Thanks mathman and dennis for your help.
Actually I'm looking for the X.

Like mathman said, it probably a typo.

Have a look at the complete solution.

[attachment=0:kckc9cf8]2013-06-22_105523.gif[/attachment:kckc9cf8]
Attached Images 2013-06-22_105523.gif (45.3 KB, 864 views) June 21st, 2013, 09:42 PM   #6
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Re: Need Help with Accumulated Value

Quote:
 Originally Posted by ajie Have a look at the complete solution.
Your complete solution attachment has: (1 + i)^20 = 4

That's what I gave you in my post: 1 + i = 4^(1/20) : SAME THING!

r = rate every 4 years = (1 + i)^4 - 1 = .3195....

Value end of 40 years = 100(1+r)[(1+r)^10-1] / r = 6194.72 June 21st, 2013, 10:03 PM #7 Newbie   Joined: Jun 2013 Posts: 3 Thanks: 0 Re: Need Help with Accumulated Value Thanks Denis, I could sleep well now.  June 22nd, 2013, 06:44 AM #8 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 Re: Need Help with Accumulated Value This can be made really simple, once we have determined that annual rate = 4^(1/20) - 1 = .071773 or 7.1773% This rate is adjusted to coincide with the frequency of the $100 deposits, which is every 4 years: i = [4^(1/20)]^4 - 1 = .319508 or 31.9508% It is now easy to see that the immediate deposit of$100 will accumulate to 131.9508 by the end of first 4-year period. So now we can treat this 131.9508 as a deferred (no immediate deposit) annuity of 131.9508 over 10 periods. So we have: A = 131.9508 n = 10 i = .319508 F = ? (F being Future value) Formula is: F = A[(1 + i)^n - 1] / i so: F = 131.9508[(1 + .31950 ^10 - 1] / .319508 = 6194.71944... And will look like, in bank statement format: Code: N:YEAR DEPOSIT INTEREST BALANCE 0 : 0 .00 1 : 4 131.95 .00 131.95 2 : 8 131.95 42.16 306.06 3 :12 131.95 97.79 535.80 .... 9 :36 131.95 1,080.62 4,594.72 10:40 131.95 1,468.05 6,194.72 Tags accumulated Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post BrianMX34 Calculus 1 December 11th, 2012 08:49 PM king.oslo Calculus 2 February 5th, 2012 02:03 PM

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