question 7 the corner bar & grill is in the process of taking a five - year loan of $50,000 at an annual…

question 7 the corner bar & grill is in the process of taking a five - year loan of $50,000 at an annual interest rate of 8% with first community bank. the loan requires 5 equal payments at the end of each year inclusive of interest and part of the principal. find the total interest payments over the life of the loan. (round your answer to the nearest dollar) a $4,000 b $12,523 c $12,614 d $20,000 e none of the other choices question 8 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 1.5 points 1.5 points

question 7 the corner bar & grill is in the process of taking a five - year loan of $50,000 at an annual interest rate of 8% with first community bank. the loan requires 5 equal payments at the end of each year inclusive of interest and part of the principal. find the total interest payments over the life of the loan. (round your answer to the nearest dollar) a $4,000 b $12,523 c $12,614 d $20,000 e none of the other choices question 8 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 1.5 points 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 $C$ is the cash - flow per period and $r$ is the interest rate. Given $C = 1000$ and $r=0.1$, then $PV_{perpetuity}=\frac{1000}{0.1}=10000$.

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 $n = 20$. First, calculate $(1 + 0.1)^{-20}=1/1.1^{20}\approx0.148644$. Then, $1-(1 + 0.1)^{-20}=1 - 0.148644 = 0.851356$. $\frac{1-(1 + 0.1)^{-20}}{0.1}=\frac{0.851356}{0.1}=8.51356$. $PV_{annuity}=1000\times8.51356 = 8513.56$.

Step3: Find the difference

The difference $\Delta PV=PV_{perpetuity}-PV_{annuity}=10000 - 8513.56=1486.44\approx1486$. Since the closest answer among the options is not provided exactly, we assume there might be some rounding differences in the problem - setup. But following the correct financial - mathematics approach, we have completed the necessary calculations.

Answer:

There is an error in the provided options as the calculated value does not match any of them. But if we were to choose the closest one based on the work above, we note that the closest value to our calculated difference of approximately $1486$ is not present among the given choices, so the answer would be E. None of the other choices.