For continuous compounding, e

You want to find t for r=6% and e

2 = e

Ln[2] = .06t

Ln[2]/.06 = t

.693147/.06 = t = 11.55

It will take 11.55 years at 6% per year to double your money.

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"9 years" has nothing to do with the problem of doubling your money. Nor does $3000. The multiplier for 9 years is

e

$3000 will be worth $3000*1.716007 = $5148.02 after 9 years.

^{rt}gives the multiplier for your money, given an interest rate r and a time interval t.You want to find t for r=6% and e

^{rt}=2.2 = e

^{.06t}Ln[2] = .06t

Ln[2]/.06 = t

.693147/.06 = t = 11.55

It will take 11.55 years at 6% per year to double your money.

_____

"9 years" has nothing to do with the problem of doubling your money. Nor does $3000. The multiplier for 9 years is

e

^{(.06)(9)}= e^{.54}≈ 1.716007$3000 will be worth $3000*1.716007 = $5148.02 after 9 years.