Financial math (1 Viewer)

[mitchy_boy]

my teacher gave me this question, and I can't do it. Don't laugh.

ok so say you have $500,000 in capital and you invest it at 3%p.a. and each year $30,000 is deducted. how long will it take for the original amount to reduce to $200,000? i was trying to rework the A=P(1+i)^n formula by putting a -30,000n into it but it doesn't seem to be working.

if u could show working that would be awsome

 

[gurmies]

First year ===> $500,000(1.03) - $300,000

Second year ===> [$500,000(1.03) - $30,000](1.03) - $30,000

= $500,000(1.03)^2 - $30,000(1+1.03)

If you continue this, you'll notice that the pattern is $500,000(1.03)^n-$30,000[1+1.03+1.03^2+...+1.03^(n-1)] <=== Sum of a G.P.

So $500,000(1.03)^n - $30,000(1.03^n-1)/(0.03) is the expression; where n represents years.

$200,000 = $500,000(1.03)^n - $30,000(1.03^n-1)/(0.03)

$6,000 = $15,000(1.03)^n - $30,000(1.03^n-1)

= $15,000(1.03)^n - $30,000(1.03)^n + $30,000

$15,000(1.03)^n = $24,000

(1.03)^n = 8/5

nln(1.03) = ln(8/5)

n = ln(8/5)/ln(1.03)

~ 15.9 years

EDIT: Ooh, Q-Dance logo =] <3 Hardstyle/Nu-Style

 

[mitchy_boy]

Ahhh thanks heaps man, thats epic

lol you gotta love hardstlye

 

[Aquawhite]

Why post this in 4U section?

It's a 2U topic/idea with a 3U twist on the end ... lol

Good question though. and good solve gurmies.

 

[mitchy_boy]

Why post this in 4U section?

It's a 2U topic/idea with a 3U twist on the end ... lol

Good question though. and good solve gurmies.

lol cos this forum gets the most responses

 

[Uncle]

lol cos this forum gets the most responses

lol because you are jew and love money.