How much money would you have to invest to make $300 within 2 years if the interest rate was 4.5%?

- anonymous

How much money would you have to invest to make $300 within 2 years if the interest rate was 4.5%?

- chestercat

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- anonymous

\[x \times 1.045^2 \geq 300 \implies x \geq \frac{300}{1.045^2}\]

- anonymous

umm so whats the answer??

- anonymous

Umm, umm, umm... the answer is do your own homework, kiddo.

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- anonymous

Or read what I posted and work out the answer for yourself.

- anonymous

Interest rate of 4.5% => value goes up by a factor of 1.045 each year.

- anonymous

but that is confusing, thats not what it shows me to do on my practice stuff

- anonymous

my practice stuff is like P = r x t stuff ... what you posted looks nothing like what im supposed to do, thats why i dont understand what u wrote

- anonymous

If m money is invested, you have 1.045m after one year, and 1.045^2 m money after two years. if this equals 300, you have m = 300/1.045^2 = 287.08 to 2 decimal places. So if you want over 300, the mimnimum amount (to the nearest $) is 288. There.

- anonymous

Where 1.045^2 = 1.045 x 1.045

- anonymous

isnt it supposed to look something like ... 300 x .045 x 2 = ??

- anonymous

Oh, you want 300 extra, not 300 in total? My mistake, sorry.
It would be m * 0.045 * 0.045 = 300
m=300/0.045^2 = 300/(0.045 * 0.45)

- anonymous

300/0.045 x 2 = ?? is that wat its supposed to be like

- anonymous

The last one was a typo, sorry again. They're both 0.045. But it's 0.045 TIMES ITSELF. Not x 2.
Sorry, so many silly mistakes by me, I was a little too mean earlier.

- anonymous

300/(0.045 x 0.045)

- anonymous

are you sure lol

- anonymous

I study Mathematics at the best University in the world. I am sure.

- anonymous

and what university is that mr.newton

- anonymous

Cambridge, England.

- anonymous

ohhh ic. My dads home england. So about that equation ... why did u do 0.045 twice??? im pretty sure i have to show the 2 in my equation

- anonymous

In the first year, it goes up by 4.5% , so you have 0.045 more. The second year, it goes up by it again, so you have ((1.045) x starting money) x 1.045) = starting money x 1.045 x 1.045 or 1.045^2. The extra money is 0.045 x 0.045 x starting money, and this is equal to 300.

- anonymous

Wait, one second. Sorry, it's about 4am here. You have 1.045 * 1.045 the starting money. If you want 300 extra, then 1.045^2 x starting money = starting money +300
So 300 = (1.045^2-1)m so m = 300/(1.045^2-1) = 300/((2.045)(0.045)).
Wow, I am so sorry. What is wrong with me today.
The answer is $3259.98 = $3260
3260 * 1.045 * 1.045 = 3560 = 3260 + 300.
WOW, sorry, I have never looked at it for the profit not total, so made a silly mistake.
Goodnight, And sorry again. fluttering hell, what's wrong with me today.

- anonymous

That is possibly the most embarrassingly bad maths I have done in my entire life.

- anonymous

wat is * ?

- anonymous

Just another symbol for times, x, I use them interchangeably :(

- anonymous

so he must invest 3259.98 to make $300 within 2 years if the interest rate was 4.5% ???

- anonymous

Yes, yes - 300/(1.045 x 1.045 - 1) = 300/(2.045 x 0.45) = 3259.98
3259.9837, to be exact, but $3260 is probably what you want.
I am going, sorry for wasting your time (and mine, I am going to have about 3 hours sleep now :/) Have a nice life.

- anonymous

ok thank you...

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