April Stigum will receive a 6 year annuity of $2,000 per year, beginning 7 years from today. In other words, the first payment will be made at the end of year 7. Assuming a required rate of return of 10%, calculate the present value today of her annuity. (Enter a positive value and round to 2 decimals
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To find the present value of an annuity, we'll use the formula for the present value of an ordinary annuity:
PV = Pmt × ( 1 - 1/(1+r)n) x r
Where:
Pmt = Payment per period = $2,000
r = Required rate of return = 10% or 0.10
n = Number of periods = 6 years
However, since the payments start at the end of year 7, we need to discount these payments back to the present value at year 0.
First, let's find the present value of the annuity:
PV = $2,000 × (1 -1/(1+0.10)6) x 1/0.10
Calculating this gives us:
PV = $2,000 × (1 -1/(1.10)6) x 1/0.10
PV = $2,000 × (1 - 1/1.77156) x 10
PV = $2,000 × (1 - 0.56447) x 10
PV = $2,000 × 0.43553 x 10
PV = $ 8710.60
Therefore, the present value today of the annuity is approximately $8,710.60 when rounded to two decimal places.