I think that the question is written poorly.
5. Assuming a 6% interest rate, how much would Danielle have to invest now to be able to withdraw $10,000 at the end of each year for the next nine years.
I came up with $166,667 using the compound interest formula assuming that n=12, t=9.
it should be clear that your answer is way off, since only $90,000 is being withdrawn over the life of the investment.
So, less than $90K will have to be invested, since the money in the fund will be earning interest. Check your formula for the present value of an annuity to get the answer.
I got 68016.92
To determine the amount that Danielle would have to invest now, we can use the concept of present value. The present value is the value of a future sum of money at its current worth. In this case, we need to find the present value of the $10,000 withdrawals at the end of each year for the next nine years, given a 6% interest rate.
To calculate the present value, we can use the present value formula:
PV = FV / (1+r)^n
Where:
PV = Present Value
FV = Future Value (the amount to be withdrawn each year)
r = Interest rate per period
n = Number of periods
In this case, the future value (FV) is $10,000, the interest rate (r) is 6% or 0.06, and the number of periods (n) is 9. Let's substitute these values into the formula:
PV = $10,000 / (1+0.06)^9
Calculating this equation, we get:
PV = $10,000 / (1.06)^9 = $10,000 / 1.719993674
Therefore, the present value (amount Danielle would have to invest now) is approximately $5,814.50.
So, Danielle would have to invest approximately $5,814.50 now in order to be able to withdraw $10,000 at the end of each year for the next nine years, assuming a 6% interest rate.