V P3-10. Calculating Present Value of a Savings Fund. (Obj. 5)

Hal Thomas wants to establish a savings fund from which a community organization could draw $850 a year for 45 years. If the account earns 6 percent, Hal will have to deposit $ now to achieve this goal.

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To calculate the present value of a savings fund, we will use the formula for calculating the present value of an annuity.

The formula for calculating the present value of an annuity is:

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

Where:
PV = Present value of the annuity
PMT = Payment or amount to be withdrawn annually
r = Interest rate per period
n = Number of periods

In this case, Hal wants to establish a savings fund from which $850 will be withdrawn annually for 45 years. The account earns a 6 percent interest rate.

Let's plug the values into the formula:

PMT = $850
r = 6% or 0.06
n = 45

PV = $850 x (1 - (1 + 0.06)^-45) / 0.06

Now let's solve this equation to find the present value:

Step 1: Calculate (1 + 0.06)^-45
(1 + 0.06)^-45 = 0.2004 (rounded to four decimal places)

Step 2: Calculate (1 - 0.2004)
1 - 0.2004 = 0.7996 (rounded to four decimal places)

Step 3: Calculate PV
PV = $850 x 0.7996 / 0.06
PV = $11,996.67 (rounded to two decimal places)

Therefore, to achieve Hal's savings goal of $850 annually for 45 years at an interest rate of 6 percent, he will need to deposit $11,996.67 now.