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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