Suppose an annuity will pay $18,000 at the beginning of each year for the next 8 years. How much money is needed to start this annuity if it earns 6.9%, compounded annually?

Do annuity payments stop at death? Or is lump sum payment made to a beneficiary? If either case, age and actuarial data on life expectancy are needed.

The present value of the annuity (due)

An=P*(1-v^n)/(1-v) where v=1/(1+i)
P=18000, n=8, i=0.069

A8=115346

To calculate the amount of money needed to start the annuity, we can use the formula for the present value of an ordinary annuity. The formula is:

PV = PMT × [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present value (the amount of money needed to start the annuity)
PMT = Payment per period ($18,000 in this case)
r = Interest rate per period (6.9% or 0.069 in decimal form)
n = Number of periods (8 years in this case)

Let's substitute the given values into the formula:

PV = $18,000 × [(1 - (1 + 0.069)^(-8)) / 0.069]

Now, we can solve this equation to find the present value (PV).