Hal Thomas wants to establish a savings fund from which a community organization could draw $800 a year for 20 years. If the account earns 3 percent, what amount would he have to deposit now to achieve this goal? (Round time value factors to 3 decimal places and final answer to 2 decimal places. Omit the "$" sign in your response.)
11907
To find the amount that Hal Thomas would have to deposit now, we can use the concept of present value. Present value is a financial calculation that determines the current worth of a future cash flow, considering the time value of money.
In this case, Hal Thomas wants to establish a savings fund where he can withdraw $800 per year for 20 years. The interest rate for the fund is 3 percent.
We can use the present value of an ordinary annuity formula to calculate the amount Hal Thomas needs to deposit now. The formula is as follows:
PV = PMT * [(1 - (1 + r)^-n) / r]
Where:
PV = Present Value (the amount Hal Thomas needs to deposit now)
PMT = Payment amount per period ($800)
r = Interest rate per period (3% or 0.03)
n = Number of periods (20 years)
Let's substitute these values into the formula and calculate the present value:
PV = $800 * [(1 - (1 + 0.03)^-20) / 0.03]
First, let's calculate (1 + 0.03)^-20:
(1 + 0.03) = 1.03
1.03^-20 = 0.553678695
Now substitute this value into the formula:
PV = $800 * [(1 - 0.553678695) / 0.03]
PV = $800 * (0.446321305 / 0.03)
PV = $800 * 14.87737683
PV ≈ $11,901.90
Therefore, Hal Thomas would need to deposit approximately $11,901.90 now in order to achieve his goal of providing $800 per year to the community organization for 20 years, assuming an interest rate of 3 percent.