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08 March 2010 @ 08:01 pm
ARGH! Need maths help!  
I was once good at maths.

I know I should know how to do this, but I cannot remember enough to see if my method is effective or not. I found a website that will let me punch in numbers and give me an answer, but I want to check it! So I am hoping that shocolate  or someone similarly gifted is up and about.

I start with $50. Every week, I add $50. I have a compounding interest rate of 9.96%. I compound it annually, or monthly (two results). What do I have at the end of 21 years?

More than happy to do all the actual working if someone can remind me of what the formulae are.
Jamfranalan on March 8th, 2010 09:44 am (UTC)
This doesn't seem to be too horribly wrong...

Sorry I can't be more help...I've never been any good at this type of maths. Give me triple differential equations and I'm fine. Interest rates and anything using real nulbers instead of symbols...eeeep! No can do!
blamebramptonblamebrampton on March 8th, 2010 09:56 am (UTC)
Alas, doesn't work for the continual additions.

It shouldn't be that hard ... but I can't do it!

Really it's:
50*52*21 (the amount per week, times weeks, times years), plus
1.0083*50*251 (monthly interest rate, times first month's money, times all months bar the first, plus
(1.0083 squared)*50*250, plus
(1.0083 cubed)*50*249, plus ...

And I KNOW I can work out how to do this, if only I could remember how!

Weeks in 21 years - edm on March 8th, 2010 10:18 am (UTC) (Expand)
Re: Weeks in 21 years - blamebrampton on March 8th, 2010 11:29 am (UTC) (Expand)
Ewen McNeilledm on March 8th, 2010 09:45 am (UTC)
I've never studied finance in detail, so I may be overlooking some summary formula, but I've always solved such savings problems with brute force, viz by calculating a series of weekly totals taking the new deposits into account and the new interest (eg, one week's fraction of the annual interest) into account as appropriate. (FWIW, the wikipedia compounding interest page assumes unchanged principal, just interest being added, as does this textbook chapter.) Any programing language, or even a big spreadsheet, allows that sort of iteration (it's only about 1000 rows providing you don't want daily compounding).

Note that IME most savings accounts are actual daily compounding, with interest credited 1-4 times a year, rather than only compounding once or twice a year. But given your hypothetical interest rate (9.96%! does anyone pay even half that these days?!) perhaps you have a hypothetical account too that really does only compound once or twice a year.

My brute force perl script suggests that with weekly compounding (irrespective of when it's credited), you'd have over $185,000 at the end (with exactly how much depending a bit on the details of leap years you happen to cross, and hence number of weeks involved). This calculator suggests you'd have a bit over $174,000 if the interest were only compounded annually (alas it doesn't have a biannual compounding option, only daily/monthly/quarterly, but the figure ought to be somewhere in between those two values -- or more precisely between the quarterly and yearly figures).

I hope that helps,


PS: Of those amounts about $55,000 is weekly cash contributions and the rest is interest. (1.0996)^21 is nearly 7.5 (so approx 7500%), but obviously not all of the cash is there at the start to get interest, so figures in the $170,000-$185,000 range are quite believable.
Ewen McNeilledm on March 8th, 2010 09:54 am (UTC)
Re: Interest
PPS: The above assumes that you are getting 9.96% after tax, an even less believable situation. If your tax rate is, eg, 33% then the effective annual interest rate is closer to 6.6% and the totals will correspondingly be much smaller. Although typically the tax is only deducted when the interest is credited, not when it is compounded, so daily compounding with annual crediting can work out slightly better from this point of view. (If you're getting 9.96% interest after tax, at present, I'd be very cautious about the risk of the investment -- the chances of ending up with $0 would seem noticeably high.)


Re: Interest - blamebrampton on March 8th, 2010 10:02 am (UTC) (Expand)
Sherrysherryillk on March 8th, 2010 09:58 am (UTC)
Try this: http://www.mathhelpforum.com/math-help/business-math/60410-i-have-question-annuity-calculation.html

It seems to be along the lines you are looking for... But it seems to yield a pretty bad-ass looking equation that makes me want to run for the hills... >
blamebramptonblamebrampton on March 8th, 2010 12:37 pm (UTC)
Cheers dear! Alas, it does not work for me when m>c :-(
(no subject) - sherryillk on March 8th, 2010 01:20 pm (UTC) (Expand)
(no subject) - blamebrampton on March 8th, 2010 01:24 pm (UTC) (Expand)
(no subject) - sherryillk on March 8th, 2010 01:38 pm (UTC) (Expand)
Loyaulte Me Lieshocolate on March 8th, 2010 12:04 pm (UTC)
*buckles under the pressure*

having a maths degree doesn't seem to help in the Real World...
blamebramptonblamebrampton on March 8th, 2010 12:38 pm (UTC)
HEE! Well, to be honest, the only thing degrees in English and Philosophy are good for is coming up with convincing explanations for why you're late for work ...
(no subject) - oceaxe on March 8th, 2010 10:05 pm (UTC) (Expand)
(no subject) - blamebrampton on March 8th, 2010 10:07 pm (UTC) (Expand)
(no subject) - oceaxe on March 8th, 2010 10:12 pm (UTC) (Expand)
Hueyphoenixacid on March 8th, 2010 12:30 pm (UTC)
If I remember it correctly,

By year:

Firstly, we calculate the amt of savings in a year = $50 X 4 weeks X 12 months = $2400

Total savings at the end of 1st yr
= 2400 + (9.66/100)(2400)
= 2400(1.0966)

Total savings at the end of 2nd yr
= (2400 + 2400(1.0966))(1.0966)
= 2400 (1.0966 + 1.0966^2)

Total savings at the end of 3nd yr
= (2400 + 2400(1.0966) + 2400(1.0966)^2)(1.0966)
= 2400 (1.0966 + 1.0966^2 + 1.0966^3)

Total savings at the end of 21st yr
= 2400 (1.0966 + 1.0966^2 + 1.0966^3 + ... + 1.0966^21)
= 2400 (1.0966 [1.0966^21 -1]/[1.0966 -1]
= 161682.8889

(using the summation formula of geometric progression, Sn = a(1-r^n)/(1-r))

Similar for month...

I have no idea how accurate this is. It's what I learn in secondary school (and I'm now doing applied math and not finance lol)

Hueyphoenixacid on March 8th, 2010 12:32 pm (UTC)
Oh, it's Sn = a(r^n-1)/(r-1)) if |r| >= 1, that's why we use it the other way around....
(no subject) - blamebrampton on March 8th, 2010 12:36 pm (UTC) (Expand)
(no subject) - phoenixacid on March 8th, 2010 12:41 pm (UTC) (Expand)
(no subject) - blamebrampton on March 8th, 2010 12:48 pm (UTC) (Expand)
(no subject) - phoenixacid on March 8th, 2010 12:58 pm (UTC) (Expand)
(no subject) - phoenixacid on March 8th, 2010 01:06 pm (UTC) (Expand)
(no subject) - blamebrampton on March 8th, 2010 01:10 pm (UTC) (Expand)
κάτι τρέχει στα γύφτικα_inbetween_ on March 8th, 2010 01:09 pm (UTC)
Since this sounds exactly like the deal the bank pestered me about, I'd like to add that if then withdrawn at once and not paid monthly till your death, it won't be 10 percent but much less plus more taxes. I'd be happy if I'm mistaken about the deal you're considering, and hope you do live to see 100 and make them pay till then, hah.
blamebramptonblamebrampton on March 8th, 2010 01:11 pm (UTC)
Heh! Well, people in my family often do live over 100 ... Nah, it's for a magazine article, purely hypothetical :-)
(no subject) - _inbetween_ on March 8th, 2010 01:14 pm (UTC) (Expand)
The Ramblings of an often very distracted person.annes_stuff on March 8th, 2010 01:26 pm (UTC)
When do you need it?

I might be able to work it out using Excel.
blamebramptonblamebrampton on March 8th, 2010 01:31 pm (UTC)
Ta luv ;-) Mr B has offered to do it if he stops killing aliens before 1. *Gives him A Look*
(no subject) - annes_stuff on March 8th, 2010 01:34 pm (UTC) (Expand)
some kind of snark faeryshyfoxling on March 8th, 2010 09:52 pm (UTC)
What I wanna know is where the heck you are getting an interest rate that fantastic, since my best account right now is slightly above 2%.
blamebramptonblamebrampton on March 8th, 2010 09:56 pm (UTC)
All hypothetical. Though if you want something good at the moment, see if you can invest in the Australian Stock Exchange, it's trending nicely. Buy in after a US-led dip ;-)
(no subject) - blamebrampton on March 8th, 2010 09:57 pm (UTC) (Expand)
Oalethiaxx on March 9th, 2010 12:22 am (UTC)
I'm fairly certain you just combine the formulas for capital accumulation and future value of a series:
Balance = P(1+i)^n + c/i[(1+i)^n-1]
P=principal, i=interest/period, n=# periods, c=contribution/period

You've probably figured it all out by now, though :)
bare_memabonwitch on March 9th, 2010 06:01 am (UTC)
Er...my sole contribution is that my work calculates weeks per month as 4.3. Good luck!
uminohikariuminohikari on March 9th, 2010 09:22 pm (UTC)
The only problem is that months and weeks don't match up exactly D: So unless you just use brute force, you'd end up with pretty crazy equations..