Use logs and exponents to solve application problem

Question

If 100 dollars is invested into an account making 3 percent annual interest compounded monthly. How long until the account contains 135 dollars? Round to the nearest tenth of a year.

Answer 1

 A  = P (1 + r/n)^nt                 compound interest formula

135 = 100 (1 + .03/12)^12t    substituting given values, then solve for t

1.35 =        (1.0025)^12t          divide both sides by 100, also simplify the 1 + .03/12 = 1.0025

ln(1.35) = ln(1.0025)^12t       natural log of both sides, the answer to all of life’s questions!

ln(1.35) = 12tln(1.0025)      power rule

Now, divide both sides by 12ln(1.0025) to get:

t =

t = 10.0159 or 10 years