ARGH! Need maths help!

[blamebrampton]

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.

Comments

[franalan.livejournal.com]

This doesn't seem to be too horribly wrong...
http://en.wikipedia.org/wiki/Compound_interest

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!

Interest

[ewen]

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,

Ewen

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.

[sherryillk.livejournal.com]

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... >

[shocolate.livejournal.com]

*buckles under the pressure*

having a maths degree doesn't seem to help in the Real World...

[phoenixacid.livejournal.com]

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)

[http://users.livejournal.com/_inbetween_/]

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.

[annes-stuff.livejournal.com]

When do you need it?

I might be able to work it out using Excel.

[arcanetrivia]

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%.

[alethiaxx.livejournal.com]

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 :)

[mabonwitch.livejournal.com]

Er...my sole contribution is that my work calculates weeks per month as 4.3. Good luck!

[uminohikari.livejournal.com]

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..