the question is in how many years?

Question

Find the time it takes for $8,800 to double when invested at an annual interest rate of 9%, compounded continuously.

Answer 1

New principal = principal * ( 1+ r)^t

2 = (1.09)^t <--- since the principal doubles, the new principal divided by the old

principal is just 2; Also (1 + 9%) = 1 + 0.09 = 1.09

log 2 = t * log 1.09 <--- log of both sides; exponent moves in front by property of logs

t = log 2 / log 1.09 = 8.04232317269....

8 years and 2 and 1/2 weeks