Investment compounded continuously? and Save Darfur protest at Franklin Templeton Investments

Investment compounded continuously?

A) An investment is made at 5.676% per year (SAI rate), compounded continuously. What is the doubling time? Round to the nearest year.

B) The doubling time of a certain bacteria culture is 8 hours. What is the growth rate (k)? Round to the nearest tenth of a percent.


Investment best answer:

Answer by cidyah
A)
Let A be the investment
A = e^0.05676 t
It the interest doubles, 2A = A e^0.05676 t
Divide both sides by A
2 = e^0.05676 t
Solve for t
ln(2) = 0.05676 t
t = ln(2) / 0.05676 = 12.21

t = 12.2 years (doubling time)

B)
P(t) = P(0) e^kt, where P(0) is the initial value
P(t) is the value at time t
When t=2, P(t) = 2P(0)

2P(0) = P(0) e^2k
divide both sides by P(0)
2 = e^2k
ln(2) = 2k
k = ln(2) / 2

k = 0.34657 (growth rate)

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