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

[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)

[phoenixacid.livejournal.com]

Oh, it's Sn = a(r^n-1)/(r-1)) if |r| >= 1, that's why we use it the other way around....

[blamebrampton.livejournal.com]

For the annual, yes. For the monthly, sadly no, because it's compounded monthly on a principle increased weekly. AND I CAN'T DO EEEET!

*Weeps at yet another area of stupidity ...*

[phoenixacid.livejournal.com]

It should be the same?

amt of savings in a month = $50 X 4 weeks = $200

Total savings at the end of 1st month
= 200 + (9.66/100)(200)
= 200(1.0966)

... and so on for 21X12 months?

Or did I get your question completely wrong?

Compounded monthly on a principle increased weekly... erm, sorry does it mean you +50 weekly and the interest per month is 9.96%?

(this is what happens when you learn high school maths in Malay)

[blamebrampton.livejournal.com]

+50 weekly, interest will be 0.83% per month 9.96/12, but then there aren't always 4 weeks in a month and Argh! It's nearly midnight, I'll have coffee and handle it in the morning. When I am sure it will be magically easy!

[phoenixacid.livejournal.com]

Lol, good luck, hon. I'm sorry I can't be more help; it's nearly bedtime for me too. :) Have a good rest alright!

[phoenixacid.livejournal.com]

BTW is the answer 163840.8696 using your online calculator? (I used the formula I've given above)

[blamebrampton.livejournal.com]

No, but I think that if we factor in the extra weeks, it would be quite close ;-)