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

[blamebrampton.livejournal.com]

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

[ewen]

FWIW, there are more than (52 * 21) = 1092 weeks in 21 years. There's more like (((365*21)+5) / 7) = 1095 weeks (actually over 1095.5 weeks; and depending on how the leap years fall there could be one more day in those 21 years). Just one of the annoying things about trying to do financial calculations on a weekly basis with rates that are yearly. (Payroll calculations for, eg, monthly allowances paid weekly are even more annoying; such things should be prohibited by the Geneva Convention.)

The formulas here (which was suggested by sherryillk) look plausible, and pretty simple to calculate (no series calculations), but I've not done enough finance to be sure of the derivation. (Hence using brute force to solve such problems.)

Ewen

Re: Weeks in 21 years

[blamebrampton.livejournal.com]

Quite right! And, as I realised after the first three minutes of trying to check independently, the money goes in weekly and is compounded monthly, so that won't fit easily unless I take an average monthly amount, which I may as well do, actually ...

Back to sherryillk's formula! It wouldn't work for me for m>c, but maybe it will if m=c!

I knew I would regret not practicing my maths as much as my French and Italian one day!