For this problem, use an annual interest rate of 4%.

On 1/1/2020, you buy a perpetuity paying you $10,000 at the beginning of each year, commencing on 1/1/2020. (Recall that a perpetuity is an annuity that does not end.)

(a) Calculate the present value of the perpetuity as of 1/1/2020.

(b) After receiving exactly ten payments, you exchange the perpetuity on 1/1/2030 for an annuity paying $x at the beginning of each year for 20 years, commencing on 1/1/2030. (Note: Since you have received exactly ten payments, you exchange your perpetuity on 1/1/2030 before receiving the payment of $10,000 on that day.)

What is the present value of your perpetuity on 1/1/2030 when you exchange it?

(c) Without any calculations, conclude whether $x is greater than, equal to, or less than $10,000. Explain.

(Note: A correct answer without a correct explanation earns no credit.)

(d) Calculate $x.