Jamie invests $500 in an account that is compound continuously at an annual rate of 5% according to the formula A=Pe^rt, where A is the amount accrued, P is the principal, r is the rate of interest and t is the time in years. approximately how many years will it take Jamie's money to double?

1000=500e^(.05)t
2=e^.05t
ln2=.05t
t=13.9

yes

To solve this problem, we can use the formula for continuous compound interest:

A = Pe^(rt)

In this case, Jamie invests $500, so P = $500. The annual interest rate is 5% or 0.05, so r = 0.05. We need to find the value of t, the time it takes for the investment to double.

We can rewrite the formula as:

2P = Pe^(rt)

Dividing both sides of the equation by P, we get:

2 = e^(rt)

Now, we can take the natural logarithm (ln) of both sides to isolate the exponent term:

ln(2) = rt ln(e)

Since ln(e) is equal to 1, the equation simplifies to:

ln(2) = rt

Now, we can solve for t. Divide both sides of the equation by r:

t = ln(2) / r

Substituting the values, we get:

t = ln(2) / 0.05

Using a calculator, we find that ln(2) ≈ 0.693147181, so:

t ≈ 0.693147181 / 0.05 ≈ 13.9

Therefore, it will take approximately 13.9 years for Jamie's money to double.