Question

you have just won a small lottery. it will pay you either 5 annual payments of $15,000 each (with the first payment to be received two years from today), or a single lump sum to be received today. if you can invest at a 6% annual rate of interest, what is the least you should accept as the lump sum payout amount?

Answer 1

To determine the least lump sum payout amount, you need to compare the present value of the annuity payments to the present value of the lump sum. The present value of the annuity payments is approximately $63,458, while the present value of the lump sum is approximately $25,619.

Step-by-step explanation:

To determine the least lump sum payout amount, we need to compare the present value of the annuity payments to the present value of the lump sum.

Present value of annuity payments:

The present value of an annuity formula can be used to calculate the present value of the $15,000 annual payments over 5 years at 6% interest rate. Plugging in the values, we get:

1. n = 5 (number of years)
2. i = 6% (interest rate)

The present value of the annuity payments is approximately $63,458.

Present value of lump sum:

The present value of a lump sum formula can be used to calculate the present value of the lump sum at 6% interest rate. Plugging in the values, we get:

1. n = 2 (number of years)
2. i = 6% (interest rate)

The present value of the lump sum is approximately $25,619.

Therefore, to be indifferent between the two options, you should accept a lump sum payout amount greater than $63,458.