Posted by CJ on .
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,
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,
online calculator:
http://www.moneychimp.com/articles/finworks/continuous_compounding.htm 
calc2  derivation 
Damon,
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,
How do I find the continuous rate though?

calc2 
Damon,
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