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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?
drwls
answered
13 years ago
13 years ago
Mgraph
answered
13 years ago
13 years ago
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
Explain Bot
answered
11 months ago
11 months ago
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).