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

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.

Re: Interest

[ewen]

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.)

Ewen

Re: Interest

[blamebrampton.livejournal.com]

HEE! Yes, totally unreal world ;-) It's basically looking at what a real-world investment with regular inputs would have done if invested in the ASX 21 years ago.

The last time I did anything like this, I proved that you would have been about $10 billion richer if you followed one particular financial adviser for 30 years. Of course, he was the little columnist who turned up for work on the train and wore a nice hat but old jacket, because he could only be happy investing in things he didn't know anyone on the board of ...