Question

Rick invested money in a continuous compound account with an interest rate of 3%. How long will it take for Rick’s account to double?

Answer 1

A = Pe^(rt)

Let A = 2P

Let r = 0.03

2P = Pe^(0.03t)

We need to find t.

2P/P = e^(0.03t)

2 = e^(0.03t)

Take the natural log on both sides.

ln(2) = ln(e^(0.03t)

ln(2) = 0.03t

ln(2)/0.03 = t

23.1049060187 = t

You did not indicate what we are talking about. I will assume weeks or months.

So, t is about 23 weeks or 23 months.