If you invested $500 into a bank account earning continuously compounded interest and the value after 6 years is $614.99, find the interest rate. write your answer as a percent rounded to the nearest hundredth.

r = 3.45%

Step-by-step explanation:

You need the formula for continuously compounding interest, which is

A = Pe^(rt) , where

A is the total amount of money in the account,

P is the initial investment

e is a constant that represents continuous growth

r is the interst rate as a decimal (which we will be solving for)

t is how many years the interest was compounded

Plug in the given information

 614.99 = 500e^(r6)           (we need to solve for r)

614.99/500 = e^(6r)           (divide both sides by 500, simplify the righ side)

      1.22998 = e^(6r)       (simpligy the left side)

When using 'e', we can take the natural log of both sides of the equation and use rules for logarithms to simplify further...

 ln (1.22998)  =  ln (e^(6r)

     ln (1.222998) = (6r)(ln e)      (exponent rule for natural logs lets us bring

                                                     down any exponents as multipliers  

     ln (1.22998) = 6r                 (ln e = 1, you can verify this on your calculator)

   ln (1.22998)/6 = r        (divide both sides by 6 to isolate r)

     .034499652 = r          (Use a calculator to simplify the left side)

We need to write r as a percent, rounded to the nearest hundredth, so multiply r by 100%, then round

  (0.034499652)(100%) =   3.4499652%  

Rounding gives 3.45%

r and t.

both are 64 degrees.