If $850 grows to $1,125 at an interest rate of 12.6% compounded continuously how long has the money been in the account

the money has been in the account for over 2 years.

Step-by-step explanation:

The formula for continuously compounded interest expressed as FV = PV x e (i x t) ,

Where

FV represents the future value of the investment.

PV represents the present value or initial amount that was invested.

i represents the interest rate,

t represents the time in years,

e represents the mathematical constant approximated as 2.7183

From the information given,

FV = $1125

PV = $850

i = 12.6% = 12.6/100 = 0.126

Therefore

1125 = 850 × 2.7183^0.126t

1125/850 = 2.7183^0.126t

1125/850 = 2.7183^0.126t

Raise both sides of the equation to the power of 1/0.126. It becomes

(1125/850)^1/0.126 = 2.7183^t

9.25 = 2.7183^t

t = 2.2