After what time period would the interest earned equal the original principal

Question

in an account paying 6% compounded daily?

Answer 1

Exact wording of the problem implies you're getting 6% per day:

P = Po*1.06^t

2Po = Po*1.06^t

2 = 1.06^t

ln(2) = ln(1.06^t)

ln(2) = t*ln(1.06)

t = ln(2)/ln(1.06)

t = about 11.89566

Answer:  In about 12 days

 

If the problem is asking about an annual interest rate of 6%, compounded daily, then:

P = Po*(1+0.06/365)^t

2Po = Po*(1+0.06/365)^t

2 = (1+0.06/365)^t

2 = (1+0.00016438356)^t

2 = (1.00016438356)^t

ln(2) = ln(1.00016438356^t)

ln(2) = t*ln(1.00016438356)

t = ln(2) / ln(1.00016438356)

t = 4216.9919 (days)

4216/365 = 11.5534 (years)

11*365 = 4015

4216-4015 = 201

Answer:  In about 11 years 201 days.