How long will it take an investment to double in value if the interest rate is 8% compounded continuously?

Question

anonymous · Answer

How long will it take an investment to double in value if the interest rate is 8% compounded continuously?

kropot72 · Answer

$$A=Pe ^{rt}$$
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
t = number of years
A = amount after time t
$$\frac{A}{P}=e ^{rt}=e ^{0.08t}=2$$ Now you need to solve for t.

kropot72 · Answer

@kglaguardia Do you know how to solve for t?

anonymous · Answer

$$2=ln e ^{0.08t}$$...lets you bring down the exponent so it would be $$2=0.08t \ln e$$...bring over the 0.08 and lne is equal to 1

kropot72 · Answer

$$e ^{0.08t}=2$$
Taking natural logs of both sides gives:
$$0.08t=\ln 2$$
$$t=\frac{\ln 2}{0.08}$$

anonymous · Answer

right. forgot about the other side.