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(7569)   (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  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=268000 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 0.0707486568871655, -4.07074865688717.
Here's your graph:
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