SOLUTION: Hi, Please help me solve this problem: The formula for computing the amount A of an investment of principal P invested at interest rate r for 1 year and compounded semiannual

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Question 107036: Hi,
Please help me solve this problem:
The formula for computing the amount A of an investment of principal P invested at interest rate r for 1 year and compounded semiannually is A=P(1+r/2)^2. Approximately what interest rate is necessary for $1,000 to grow to $1,075 in 1 year if the interest is compounded semiannually?
Thank you!
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
A=P(1+r/2)^2
1072=1000(.5r+1)^2
1072=1000(.25r^2+r+1)
1072=250r^2+1000r+1000
250r^2+1000r-72=0
2(125r^2+500r-36)=0
r=-4.07075 not an answer because the rate has to be positive.
r=.07075...(see below)
Check:
1000(1+.070749/2)^2=1000*(1.035374...)^2=1000*1.072=1072
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 125x%5E2%2B500x%2B-36+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28500%29%5E2-4%2A125%2A-36=268000.

Discriminant d=268000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-500%2B-sqrt%28+268000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28500%29%2Bsqrt%28+268000+%29%29%2F2%5C125+=+0.0707486568871655
x%5B2%5D+=+%28-%28500%29-sqrt%28+268000+%29%29%2F2%5C125+=+-4.07074865688717

Quadratic expression 125x%5E2%2B500x%2B-36 can be factored:
125x%5E2%2B500x%2B-36+=+%28x-0.0707486568871655%29%2A%28x--4.07074865688717%29
Again, the answer is: 0.0707486568871655, -4.07074865688717. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+125%2Ax%5E2%2B500%2Ax%2B-36+%29