Question

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

Answer 1

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

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.