# Thread: Future and Present Value

1. ## Future and Present Value

Ok. I'm just looking for some help understand how a problem is done. I'm not looking for answers. It is an example problem, but I don't understand how they arrived at the answer.

"An investor wants to have $20,000 in 9 months. If the best available interest rate is 6.05% per year, how much must be invested now to yield the desired amount?" They present the following solution: "We know that S = P + I = P + Prt. In this case, we must solve for P, the present value. Also, the time 9 months is 9/12 of a year.$20,000 = P + P(0.0605)(9/12) = P + 0.045375P

$20,000 = 1.045375P$20,000
1.045375 = P so P = \$19,131.89

Ok. I'm going to sound like sort of an idiot, but I understand where they got all of the information in line 1. I -do not- understand how they got from line 1 to line 2. Where did all of the P's go and how did they magically add 1 to 0.045375P ??

Line 2 to line 3 i get, because they divided both sides by 1.045375 to isolate P.

Any help you can offer would be much appreciated.

2. ummm.. They are just collecting like terms;
P+P=(1+1)P=2P
P+0.5P=(1+0.5)P=1.5P

Note that line 1 is;
P + P(0.0605)(9/12), or equivalently P[1+(0.0605)(9/12)]