I think {x|x < 0} is read like this: "x such that x is less than or equal to zero."
You can just read that vertical line like it says, "such that" ...that's how my teacher said it
I finally found a page that agrees with this... here . This might be a helpful page if you have any more questions about symbols like that.
I normally don't even click on these questions.. they are way outside my "comfort zone" ! ..but....I'll venture a guess......
Since it is compounded monthly...divide the annual rate by 12 (7.5/12)% = 0.625% = 0.00625
At the end of each month..there will be (1.00625 * the amount of money in the account before the company adds any that month ) in the account.
Call the monthly deposit " m "...
the amount of money after 1 month = 1.00625m
the amount of money after 2 months = 1.00625( 1.00625m + m )
the amount of money after 3 months = 1.00625( 1.00625(1.000625m + m) + m )
= 1.00625^3m+1.00625^2m +1.00625m
= m(1.00625^3 + 1.00625^2 + 1.00625)
= \(m*\sum \limits_{i=1}^{3}(1.00625^i)\)
So..after 144 months...or 12 years...there will be...
\(m*\sum \limits_{i=1}^{144}(1.00625^i)\)
Set this equal to 157,000
\(m*\sum \limits_{i=1}^{144}(1.00625^i)=157,000 \\~\\ m=157,000/(\sum \limits_{i=1}^{144}(1.00625^i))\)
And according to WA... m = 671.26
Now surely this must be a way over-complicated way of doing it..and it might be way wrong!! But...I tried!!