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%

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !