You are enormously wealthy, and would like to establish perpetuities to fund future generations of your family.

(i) Suppose that you want your child to receive a perpetuity paying $1, 000, 000 per year. Assume that your child can secure investments 1% compounded annually. Compute the present value of the perpetuity at the time that your child receives it.

(ii) Suppose that you want to establish the same perpetuity as in part (i), for each generation of your family for the next seven generations. Assume that a new generation begins every 30 years; so the perpetuities start on January 1st of the years 2020, 2050, 2080, . . ., 2200 (see the timeline). Assume that you can invest at an APR of 2%, compounded semi-annually. Calculate the total amount of money you would need to invest on January 1st, 2020 to cover the costs of these seven perpetuities. Hint: You should use your answer from part (i). Don't rederive the present value of the perpetuity.

Perp 1 Jan 1, 2020

Perp 2 Jan 1, 2050

Perp 3 Jan 1, 2080

Perp 6 Jan 1, 2170

Perp 7 Jan 1, 2200