Time value and discount rates Personal Finance Problem You just won a lottery that promises to pay you $$1,200,000$ exactly $15$ years from today. A company approaches you today, offering cash in exchange for your winning lottery ticket.

a$.$ What would you sell your claim for if you can earn the following rates of return on similar$-$risk investments during the $15-$year period? Do the values you calculated represent the lowest price you'd be willing to accept or the highest acceptable price?

$(1)5\%$

$(2)8\%$

$(3)11\%$

b$.$ Rework part a under the assumption that the $$1,200,000$ payment will be received in $20$ rather than $15$ years.

c$.$ On the basis of your findings in parts a and $b,$ discuss the effect of both the size of the rate of return and the time until receipt of payment on the present future sum.

a$.(1)$ The least you will sell your claim for if you can earn a rate of return of $5\%$ during the $15-$year period is $

$($Round to the nearest cent.$)$

$(2)$ The least you will sell your claim for if you can earn a rate of return of $8\%$ during the $15-$year period is $

$($Round to the nearest cent.$)$

$(3)$ The least you will sell your claim for if you can earn a rate of return of $11\%$ during the $15-$year period is $

$($Round to the nearest cent.$)$

The values represent the you would be willing to accept because they are based on required rates of return.

b$.(1)$ The least you will sell your claim for if you can earn a rate of return of $5\%$ during the $20-$year period is $

$($Round to the nearest cent.$)$

$(2)$ The least you will sell your claim for if you can earn a rate of return of $8\%$ during the $20-$year period is $

$($Round to the nearest cent.$)$

$(3)$ The least you will sell your claim for if you can earn a rate of return of $11\%$ during the $20-$year period is $

$($Round to the nearest cent.$)$

c$.$ On the basis of your findings in parts a and $b,$ discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of future sum. $($Select the best answer below.$)$

A$.$ As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies.

b$.(1)$ The least you will sell your claim for if you can earn a rate of return of $5\%$ during the $20-$year period is $

$($Round to the nearest cent.$)$

$(2)$ The least you will sell your claim for if you can earn a rate of return of $8\%$ during the $20-$year period is $

$($Round to the nearest cent.$)$

$(3)$ The least you will sell your claim for if you can earn a rate of return of $11\%$ during the $20-$year period is $

$($Round to the nearest cent.$)$

c$.$ On the basis of your findings in parts a and $b,$ discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum. $($Select the best answer below.$)$

A$.$ As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies.

B$.$ As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the greater the present value due to the greater time over whict the opportunity cost applies.

C$.$ As the discount rate increases, the present value becomes smaller. Also, the shorter the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies.

D$.$ As the discount rate increases, the present value becomes larger. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies.

Time value and discount rates Personal Finance Problem You just won a lottery that promises to pay you $$1,200,000$ exactly $15$ years from today. A company approaches you today, offering cash in exchange for your winning lottery ticket.

a$.$ What would you sell your claim for if y