Thomas is considering the purchase of two different annuities. The first begins in three years and pays $1,000 per year for five years. The second begins in 10 years and pays $2,500 per year for seven years. Thomas is currently very risk-averse as he has a young family and little income, and thus his current opportunity cost of capital is 4%. In nine years, Thomas expects to be more financially secure and his cost of capital will increase to 9% from then on. If each annuity costs $5,000 today, which annuity (or annuities), if any, should Thomas purchase? How much value will Thomas realize from his purchase(s), if he makes any purchases? Show work