# $A = Pe^{rt}$? How do I properly calculate this?

So, I have a word problem that I need to use the formula $A = Pe^{rt}$ to solve...

Suppose $2000 is invested at an interest rate 2.75% compounded continuously. What is the balance in the account after 4 years? Round answer to the nearest cent. I know that... $$P = \2000\\ R = 2.75\%\\ T = 4$$ What I'm trying to do is calculate this using my TI-83 and I believe the way to do this is by first multiplying 2.75(4), then press the$e^x$button, plug in my answer, then multiply it by$2000$. That's my understanding of it, but what's the actual correct way to insert this problem into my calculator? • You wrote 2.75% above, but 2.78 in the description. Also, you need to make sure of precedence and that can vary on different implementations (and calculators). Is your equation p*(e^r)*t or pe^(rt)- as this makes a huge difference. Does this solve your problem? – Amzoti Oct 5 '12 at 2:21 ## 1 Answer As Amzoti said, I think correct eqn is$A=Pe^{rt}$you can plot y=2000*e^(.0275x) in a graph and use the 2nd Calc- Value commands to evaluate at$t=4$, or can use 2nd Table to check your for multiple ranges of$t$(we just use$x\$ in the ti-83).

the way you did it should be totally fine too, so long as you use the right formula.

• Alright, thanks. I tried it both ways and came up with the same answer. :) – Brandt Oct 5 '12 at 11:58