the furniture store offers you no - money - down on a new set of living room furniture. further, you may pay…

the furniture store offers you no - money - down on a new set of living room furniture. further, you may pay for the furniture in three equal annual end - of - the - year payments of $1,000 each with the first payment to be made one year from today. if the discount rate is 6%, what is the present value of the furniture payments? a $2,673.01 b $2,833.39 c $3,000.00 d $3,183.60 e none of these are correct

the furniture store offers you no - money - down on a new set of living room furniture. further, you may pay for the furniture in three equal annual end - of - the - year payments of $1,000 each with the first payment to be made one year from today. if the discount rate is 6%, what is the present value of the furniture payments? a $2,673.01 b $2,833.39 c $3,000.00 d $3,183.60 e none of these are correct

Answer

Explanation:

Step1: Identify 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. Here, $A=$1000$, $r = 0.06$, and $n = 3$.

Step2: Substitute the values into the formula

$PV=1000\times\frac{1-(1 + 0.06)^{-3}}{0.06}$. First, calculate $(1 + 0.06)^{-3}=\frac{1}{(1 + 0.06)^{3}}=\frac{1}{1.06^{3}}=\frac{1}{1.191016}\approx0.839619$. Then, $1-(1 + 0.06)^{-3}=1 - 0.839619 = 0.160381$. And $\frac{1-(1 + 0.06)^{-3}}{0.06}=\frac{0.160381}{0.06}\approx2.673012$. Finally, $PV = 1000\times2.673012=$2673.01$.

Answer:

A. $2,673.01