If Kate wants $25,000, then that's the future value.
i is the rate of change, which is 6% in this case, which is rewritten as 0.06.
P is the starting value, or what she has to originally put in, which is what we need to find.
You put times t but it's actually to the power of t, which is time.
The time in this problem is 16 years, so t is 16.
Let's rewrite the equation with the plugged in values.
25,000 = P(1 + 0.06)^16
Now simplify:
25,000 = P(1.06)^16
25,000 = P(1.06^16)
25,000 = P(2.54)
How do you find P?
Isolate the variable!
To do this, divide both sides by 2.54.
25,000 / 2.54 = 9842.52
So that means she needs to invest an original amount of $9,842.52 if she wants to have $25,000 in 16 years with a 6% interest rate per year.
Now just check your work:
25,000 = 9842.52(1 + 0.06)^16
25,000 = 9842.52(1.06^16)
25,000 = 9842.52(2.54)
25,000 = 25,000
It works!
So $9,842.52 is the correct answer.
