SOLUTION: how long would it take for 1000 deposited in an account payinv 6% interest compounded countinously to earn 200 interest

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: how long would it take for 1000 deposited in an account payinv 6% interest compounded countinously to earn 200 interest      Log On


   

Question 1206983: how long would it take for 1000 deposited in an account payinv 6% interest compounded countinously to earn 200 interest
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
how long would it take for 1000 deposited in an account payinv 6% interest
compounded countinously to earn 200 interest
~~~~~~~~~~~~~~~~~~~ 

Formula for the future value of a continuously compounded account in this problem is

    FV = 1000%2Ae%5E%280.06%2At%29,


where "t" is in years, "e" is the base of natural logarithms.


So, we write for the total

    1000 + 200 = 1000%2Ae%5E%280.06%2At%29

or

    1200 = 1000%2Ae%5E%280.06%2At%29.


Now we solve this equation, step by step, and find time "t".

    1200%2F1000 = e%5E%280.06%2At%29

    1.2 =  = e%5E%280.06%2At%29


Next, take the natural logarithm of both sides

    ln(1.2) = 0.06*t

    t = ln%281.2%29%2F0.06 = 3.038692613


So, the  ANSWER  is that the time to earn 200 interest is about 3 years.

                 (More precisely, 3 years and 15 days).

Solved.

-----------------

To see many other similar  (and different)  solved problems on continuously compounded accounts,  look into the lesson
    - Problems on continuously compound accounts
in this site.

After reading this lesson,  you will tackle such problems on your own without asking for help from outside.