Posted by CJ on Monday, May 16, 2011 at 1:06pm.
At what constant, continuous annual rate should you deposit money into an account if you want to have $1,000,000 in 25 years? The account earns 5% interest, compounded continuously. Round to the nearest dollar.

calc2  Damon, Monday, May 16, 2011 at 1:52pm
FV = Pe^Yr
where FV = future value = 1,000,000
r here = .05
Y = 25
1,000,000 = P e^(1.25)
P = 1,000,000 / 3.49
P = 286,533

calc2  Damon, Monday, May 16, 2011 at 1:54pm
online calculator:
http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

calc2  derivation  Damon, Monday, May 16, 2011 at 2:05pm
dP/dt = r P
dP/P = r dt
ln P = r t
e^ln P = e^(rt) + C
P = C e^(rt)
when t = 0, e^(rt) = 1
so C = value of P when t = 0
so
P = Po e^(rt)

calc2  CJ, Monday, May 16, 2011 at 2:24pm
How do I find the continuous rate though?

calc2  Damon, Monday, May 16, 2011 at 5:58pm
Oh, sorry
Try this, sinking fund "Continuous compounding at nominal rate r, uniform series"
http://ece.uprm.edu/~s016965/ININ%204015%20%20Analisis%20Economico%20Para%20Ingenieros/Engineering%20Economic%20Analysis%208th%20ED.pdf
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