Jane is 55 years old and considering purchasing an annuity for retirement. The force of interest, , is 0.03 and the force of mortality, , is 0.05.

2. [10] Jane is 55 years old and considering purchasing an annuity for retirement. The force of interest, 8, is 0.03 and the force of mortality, h, is 0.05. (a) [3] Calculate the APV of a fully continuous whole life annuity with annual rate of benefit $25,000 issued to Jane. (b) [3] Calculate the variance of the product in part a. (c) [4] If Jane were to instead purchase a fully continuous 10-year guaranteed life annuity with the same APV as the whole life product in part a, determine the new annual rate of benefit. 2. [10] Jane is 55 years old and considering purchasing an annuity for retirement. The force of interest, 8, is 0.03 and the force of mortality, h, is 0.05. (a) [3] Calculate the APV of a fully continuous whole life annuity with annual rate of benefit $25,000 issued to Jane. (b) [3] Calculate the variance of the product in part a. (c) [4] If Jane were to instead purchase a fully continuous 10-year guaranteed life annuity with the same APV as the whole life product in part a, determine the new annual rate of benefit