1. A person age 40 purchases a life annuity that provides 10 000 each year for life, with the first payment starting at age 41. The first 10 payments will be paid regardless of whether the annuitant is alive or not. Find a formula for the single premium.
2. A person age 40 purchases a life annuity that provides 1 per year for life with the first payment at age 65. If (40) lives to age 65 he/she will receive at least 10 payments. Nothing is paid if death occurs before age 65. Find a formula for the premium.