what is the present value of a four - year annuity of $100 per year that begins 2 years from today if the…

Explanation:

Step1: First, find the present - value of an ordinary annuity formula

The formula for the present - value of an ordinary annuity is $PV = A\times\frac{1-(1 + r)^{-n}}{r}$, where $A$ is the annuity payment, $r$ is the interest rate per period, and $n$ is the number of periods. But this annuity starts 2 years from now. First, find the present value of the annuity at the start of year 2. $A = 100$, $r=0.09$, and $n = 4$. $PV_2=A\times\frac{1-(1 + r)^{-n}}{r}=100\times\frac{1-(1 + 0.09)^{-4}}{0.09}$ $PV_2=100\times\frac{1 - 1.09^{-4}}{0.09}=100\times\frac{1-0.708425}{0.09}=100\times\frac{0.291575}{0.09}\approx323.97$

Step2: Discount $PV_2$ back to the present (year 0)

We need to discount $PV_2$ back 2 years. The formula for present - value is $PV_0=\frac{PV_2}{(1 + r)^t}$, where $t = 2$ and $r=0.09$. $PV_0=\frac{323.97}{(1 + 0.09)^2}=\frac{323.97}{1.1881}\approx272.68$

Answer:

A. $272.68$