Suppose today is January 1, 2024 and you are given two options:

a. an annuity that pays you 1000 dollars at the end of each year until January 1, 2030 starting from now;

b. a perpetuity that pays you 1000 dollars at the end of each year, but the first cash payment is at the end of year 2034.

In other words, the perpetuity starts after 10 years from today.

Which of the options do you choose if the long-term value of APR is 5% compounded annually? Does your answer change if the rate is 10%? Explain your solutions.