Question

Time value and discount rates personal finance problem you just won a lottery that promises to pay you $1,500,000 exactly 20 years from today. a company approaches you today, offering cash in exchange for your winning lottery ticket.

What is the least you will sell your claim for if you can earn the following rates of retum on similar-risk investments during the 20-year period?
(1) 9%
(2) 13%
(3) 17%

Answer 1

To determine the present value of $1,500,000 to be received in 20 years, one must discount it using the given interest rates of 9%, 13%, and 17%. The higher the interest rate, the lower the present value, because money can potentially earn more if invested at that higher rate.

Step-by-step explanation:

To find out the least amount you would be willing to sell your claim for today, given the future value of $1,500,000 in 20 years, we need to calculate the present value of that sum at different rates of return. The formula to calculate the present value is Present Value = Future Value / (1 + Interest Rate)number of years. This is a basic time value of money problem, which takes into account discount rates to find the current worth of future cash flows.

Let's calculate the present value for each of the interest rates provided:

• 9% discount rate: $1,500,000 / (1 + 0.09)20
• 13% discount rate: $1,500,000 / (1 + 0.13)20
• 17% discount rate: $1,500,000 / (1 + 0.17)20

For each of these calculations, you're using the process of discounting to determine how much a future sum of money is worth today, taking into account the potential earnings from investments at those specified rates of return. The higher the interest rate, the less you would be willing to accept today, as the potential earnings from investing the money yourself are greater.