They will need 200,000 in 18 years and they can expect a rate of return of 6 %. How much will they need to invest annually.

I would have set it up and gotten $70068.76 but then do you divide by 18?

To determine how much they will need to invest annually, you can use the concept of future value of an ordinary annuity.

First, find the future value of the investment needed in 18 years. The formula to calculate future value is:

FV = PV * (1 + r)^n

Where:
FV = Future Value
PV = Present Value (initial investment)
r = Annual rate of return (as a decimal)
n = Number of compounding periods

In this case, the future value needed is $200,000, the rate of return is 6% (or 0.06 as a decimal), and the number of compounding periods is 18 years.

Plugging in the values, we get:

$200,000 = PV * (1 + 0.06)^18

Next, rearrange the formula to solve for PV:

PV = FV / (1 + r)^n

PV = $200,000 / (1 + 0.06)^18

Calculating this, we find that PV ≈ $70068.76, which is the correct present value needed.

Now, to find the annual investment needed, we can use the present value formula for annuities:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present Value
PMT = Annual investment payment
r = Annual interest rate (as a decimal)
n = Number of periods

We know the present value needed is $70068.76, the interest rate is 6% (or 0.06 as a decimal), and the number of periods is 18 years.

Plugging these values into the formula, we get:

$70068.76 = PMT * [(1 - (1 + 0.06)^(-18)) / 0.06]

Now, solve for PMT by isolating it:

PMT = PV / [(1 - (1 + r)^(-n)) / r]

PMT = $70068.76 / [(1 - (1 + 0.06)^(-18)) / 0.06]

Calculating this, we find that PMT ≈ $4,350.11.

Therefore, they will need to invest approximately $4,350.11 annually to accumulate $200,000 in 18 years with a 6% rate of return.