you invest d dollars in a bank account that earns 5% compounded continuously. how long will it take your money to double?

It'll take take 13.8629 years to double the money.

Step-by-step explanation:

When an amount is compounded continuosly it's growth is determined by the following function:

M = C*e^ (r*t)

Where M is the final value, C is the initial value, r is the interest rate and t is the time elapsed. In this case we want a final value that is two times the initial one, therefore M = 2*C. We have:

2*C = C*e^ (0.05*t)

C*e^ (0.05*t) = 2*C

e^ (0.05*t) = 2*C/C

e^ (0.05*t) = 2

ln[e^ (0.05*t) ] = ln (2)

0.05*t = ln (2)

t = ln (2) / 0.05 = 13.8629 years

It'll take take 13.8629 years to double the money.