Calculus Interest Continuous Growth

You deposit $40,000 into an account with interest compounded annually. You check 12 years after the account opened, and the balance is $87,594. Assuming you never withdraw or deposit money, how many years after the account opened will it have $170,000?

What is the formula to figure this out? I can't find it in my notes anywhere. Thanks.

A = P(1 + R/100)^N
87594 = 40000(1 + R/100)^12
87594/40000 = (1 + R/100)^12
(1 + R/100)^12 = 2.18985
(1 + R/100) = (2.18985)^1/12
(1 + R/100) = 1.06749995
R/100 = 0.0675
R = 6.75%

Let after N years it is 170000
170000 = 40000(1 + 6.75/100)^N
170000/40000 = (1.0675)^N
(1.0675)^N = 4.25
N log 1.0675 = Log 4.25
N = Log 4.25/Log 1.0675
= 0.6284/0.02837
= 22.15 years
------

first, this is not calculus {maybe you meant Calculate.}

second, it is not continuous growth. {that uses Euler's number.}

solve for i 87594/40000 = (1+i)^12

given i is known, solve for n 170000/40000 = (1+i)^n