Future value = P * (1 + i) t Kate wants to have $25,000 in 16 years. How much does she need to invest if the interest rate is 6 percent per year?

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.