SOLUTION: How long will it take for $1,000 to be worth $1,500 at 5% interest, compounded continuously? Round your answer to the nearest hundredth of a year.

Question 1153872: How long will it take for $1,000 to be worth $1,500 at 5% interest, compounded continuously? Round your answer to the nearest hundredth of a year.
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.


1500 = ,


t is the time in years;  "e" is the base of natural logarithm,  e = 2.71828... (approx.)


================>


 = 


1.5 = 


Take the natural logarithm of both sides


ln(1.5) = 0.05*t


t =  = 8.109 = 8.11 years (rounded as required).    ANSWER

SOLVED.

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

It is a standard way to solve such problems (with continuous compounding).

MEMORIZE it as a MANTRA.

See the lesson
- Problems on continuously compound accounts
in this site.

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

The referred lessons are 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.

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