Calculus: invest $500/mo at 5%; how long until $25,000 ?

[DuNguyen]

I'm going to put $500 a month in savings at 5%. How long until I have $25000?

Year	$ In	T years later
1	500*12		500*12e^((.05)T)
2	500*12		500*12e^((.05)T-1)
3	500*12		500*12e^((.05)T-2)
4	500*12		500*12e^((.05)T-3)
...			...
T			$25000

25000=∫^T₀ f(t)dt

∫ with T on top and 0 at the bottom

 

[stapel]

I'm going to put $500 a month in savings at 5%. How long until I have $25000?

Year	$ In	T years later
1	500*12		500*12e^((.05)T)
2	500*12		500*12e^((.05)T-1)
3	500*12		500*12e^((.05)T-2)
4	500*12		500*12e^((.05)T-3)
...			...
T			$25000

25000=∫^T₀ f(t)dt

∫ with T on top and 0 at the bottom

I'm sorry, but I don't understand what you're doing in the above...?

How often is interest compounded? What formulas have they given you for annuities and such-like? How far have you gotten in applying that information?

Please be complete. Thank you!