SOLUTION: How many years will it take for an initial investment of $10,000 to grow to $35,000? Assume a rate of interest of 9% compounded continuously. Round to two decimal places.

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Question 1171044: How many years will it take for an initial investment of $10,000 to grow to $35,000? Assume a rate of interest of 9% compounded continuously.
Round to two decimal places.
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

Use the basic formula for accounts compounded continuously


    35000 = 10000%2Ae%5E%280.09%2At%29.


In this equation t is the unknown time in years.


    35000%2F10000 = e%5E%280.09%2At%29


    3.5 = e%5E%280.09%2At%29


Take the natural logarithm of both sides


    ln(3.5) = 0.09*t


    t = ln%283.5%29%2F0.09 = 13.92.


ANSWER.  In 13.92 years.


Solved.

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To see many other similar solved problems, look into the lesson
    - Problems on continuously compounded accounts
in this site, and learn the subject from there.


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

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Happy learning (!)