question 13 how much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years…

question 13 how much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? assume a 10% interest rate and cash flows at the end of each period. (round to the nearest cent) a $297.29 b $1,486.44 c $1,635.08 d $2,000.00 e none of these are correct 1.5 points

question 13 how much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? assume a 10% interest rate and cash flows at the end of each period. (round to the nearest cent) a $297.29 b $1,486.44 c $1,635.08 d $2,000.00 e none of these are correct 1.5 points

Answer

Explanation:

Step1: Calculate present - value of perpetuity

The formula for the present - value of a perpetuity is $PV_{perpetuity}=\frac{C}{r}$, where $C = 1000$ and $r=0.1$. So, $PV_{perpetuity}=\frac{1000}{0.1}=10000$.

Step2: Calculate present - value of annuity

The formula for the present - value of an ordinary annuity is $PV_{annuity}=C\times\frac{1-(1 + r)^{-n}}{r}$, where $C = 1000$, $r = 0.1$, and $n = 20$. $PV_{annuity}=1000\times\frac{1-(1 + 0.1)^{-20}}{0.1}$. First, calculate $(1 + 0.1)^{-20}=\frac{1}{(1.1)^{20}}\approx0.148644$. Then, $1-(1.1)^{-20}=1 - 0.148644 = 0.851356$. $\frac{1-(1.1)^{-20}}{0.1}=\frac{0.851356}{0.1}=8.51356$. So, $PV_{annuity}=1000\times8.51356 = 8513.56$.

Step3: Find the difference

The difference $\Delta PV=PV_{perpetuity}-PV_{annuity}$. $\Delta PV=10000 - 8513.56=1486.44$.

Answer:

B. $1,486.44$