Question 1177632: How long will it take an investment of $2,000 to reach $3,000 if it is earning 4% interest compounded annually? Round to two decimal places.
For this important question, I need to see the calculations & answers please.
Homework question from Hans Beauvoir
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! P=Po(1+r/n)^nt , where n is number of times compounded per year (1 here) and t the number of years,
Misread problem and had 4000 on my mind.
3000=2000(1+.04)^t
1.5=1.04^t
ln both sides
ln1.5=t ln 1.04
divide ln1.5/ln/1.04;t=10.34years
rule of 70 increase by 50% time is about 41/interest rate, and that would predict 10.25 years here.
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
How long will it take an investment of $2,000 to reach $3,000 if it is earning 4% interest compounded annually?
Round to two decimal places.
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Tutor @Boreal misread the problem and solved it with wrong input data.
So I came to bring the correct solution.
P = Po(1+r/n)^nt , where n is number of times compounded per year (1 here) and t the number of years,
3000=2000(1+.04)^t
1.5 = 1.04^t
Take ln (natural logarithm) of both sides
ln(1.5) = t*ln(1.04)
t = 
t = 10.34 years
At this point, you should round the years to the nearest greater integer value, which is 11,
in order for the bank would be able to make the last compounding.
ANSWER. 11 years.
Solved.
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It is strange to me to see this incorrect instruction at the end of your post,
requesting to round to two decimal places.
The correct instruction would be "round to the closest greater integer number of years".
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To see many other similar solved problems, look into my lessons at this site
- Compounded interest percentage problems
- Problems on discretely compound accounts
Learn the subject from there.
After reading these lessons, 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 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.
Happy learning (!)
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And the last notice.
Instead of saying "I need . . . " in your post, you better write "Please help me . . . " or "Please explain me . . . "
as civilized and educated persons should do when asking for help.
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