Question 1032586
Sandy is tracking the performance of one of Atlantic Cycles' savings accounts. $10,000 was deposited into this account which earns 2.25% interest compounded continuously. How many years will it take until the account balance doubles if no withdrawals or additional deposits are made? 


I  set up problem as: $20,000= $10,000*2.718281828459(.0225x). I got 32 years as answer but this was wrong. Please help.  Thank you.
<pre>Future value (A), and present value (P) amounts are INSIGNIFICANT, so they don't have to be used.
{{{A = Pe^(rt)}}}
Doubling means that A = 2P. We then get:
{{{2P = Pe^(rt)}}}
{{{2P/P = e^(rt)}}}
{{{2 = e^(rt)}}}
{{{2 = e^(.0225t)}}} ------ Substituting .0225 (2.25%) for r
{{{ln (2) = .0225t}}} ----- Converting to LOGARITHMIC (natural) form
t, or time = {{{highlight_green(matrix(1,4, (ln (2))/.0225, or, 30.80654, years))}}}
Note that 30.80654 is NOT THE SAME as 32 years. Even if it were requested that time be rounded to the nearest year, it'd be 31, not 32.