SOLUTION: Okay. I know I asked this already, and I thank you longjohnsilver for your post; but quite frankly, that makes no sense. I need some kind of basic formula for annual interest. I re

Question 4186: Okay. I know I asked this already, and I thank you longjohnsilver for your post; but quite frankly, that makes no sense. I need some kind of basic formula for annual interest. I remember learning it, but can't recall it all.
A BOND PAYS 12% ANNUAL INTEREST COMPOUNDED CONTINUOUSLY. IF $10,000 IS INVESTED INITIALLY, WHEN WILL THE BOND BE WORTH $30,000? ROUND TO NEAREST YEAR.
Found 2 solutions by longjonsilver, rapaljer:
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
OK, try this:

start with 10000.
After 1 year you have 10000*1.12 = whatever.
After another year, you have whatever*1.12 = something.
After a third year, you have something*1.12 = value
After a fourth year, you have a value*1.12 = figure
etc etc.

Work that out until you reach 30,000. It will be 10 years.

Mathematically, what we have is:

after year 1: 10000*1.12
after year 2: 10000*1.12*1.12
after year 3: 10000*1.12*1.12*1.12
after year 4: 10000*1.12*1.12*1.12*1.12
after year 5: 10000*1.12*1.12*1.12*1.12*1.12
etc

which can be written as:

after 1 year : 10000*1.12^1
after 2 years: 10000*1.12^2
after 3 years: 10000*1.12^3
after 4 years: 10000*1.12^4
after 5 years: 10000*1.12^5
... after n years: 10000*1.12^n and this has to be 30000. So:

. Taking logs:

nlog1.12 = log3
n=log3/log1.12
n=9.694

so n=10 years

jon

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
I was thinking to use the formula for interest compounded continuously

In this formula, A=$30,000, P=$10,000, r=.12, and of course t is the unknown in years.
Substituting, this gives you:

Divide both sides by 10000 to obtain

Take the ln of both sides

Divide both sides by .12, and the answer I get is
I don't have my calculator with me, but I think that is approximately 9.185 years, which rounds off to the nearest year of 9.

What do you think?
R^2
Seminole Community College
Sanford, Florida

RELATED QUESTIONS
okay i have Finals for Geometry tomorrow and i need Help like right now!!! i have know... (answered by Alan3354)
Okay I've been staring at this problem for 10 mins, and I just don't know how to get the... (answered by Alan3354)
Okay this is my last question. on this itsays... 14-2i Over 3+i. I dont know if... (answered by stanbon,ankor@dixie-net.com)
Okay this is my last question. on this it says... {{{(14-2i)/(3+i)}}} I don't... (answered by Edwin McCravy)
I need help finding the perimeter of a regular hexagon which is made up of equilateral... (answered by jim_thompson5910)
A plane leaves Chicago and flies 750 miles to New York. If it takes 2.5 hours to get to... (answered by ankor@dixie-net.com)
okay, i am doing proofs in class and i have had three tests and failed them all. Not to... (answered by Mathtut)
Hello and thank you for your help beforehand! I've been stuck on this question for a... (answered by ankor@dixie-net.com)
okay so imagine there are different types of squares making one big rectangle where would (answered by lynnlo)