Compond interest word problem

[Makman]

Homework Statement

If the total interest earned on an investment at 8.2% compounded semiannually for 8.5 years was $1,175.98, what was the original investment?

Homework Equations

A=P(1+i)^n

The Attempt at a Solution

 

[statdad]

You need to show a little work. To get started, make a list of all the quantities (P, A, i, and n) you are given in the problem; that will show you which you need to find (and may guide you to the solution process to boot)

 

[Makman]

Thank you Statdad!

This is what I had:
n = 17
i= 0.041
P= P + $1,175.98
Am I on the right track. If I am I come out with this awkward looking formula:
P+$1,175.98 = P(1+i)^n
If this is correct then what?
Many thanks

 

[statdad]

Great!
Yes, your final line

$$P + 1175.98 = P(1.041)^{17}$$

is good. If you think about this, it is simply a linear equation with $$P$$ as the variable. All you need to do is rearrange terms and solve for $$P$$.
What do you find?

 

[statdad]

Great!
Yes, your final line

$$P + 1175.98 = P(1.041)^{17}$$

is good. If you think about this, it is simply a linear equation with $$P$$ as the variable. All you need to do is rearrange terms and solve for $$P$$.
What do you find?

 

[Makman]

YES! Got it. Simple algebraic manipulation. Answer is $1,200.

Thank you very much!