19. Norma receives $400,000 from a life insurance policy with which she purchases an annuity-certain. The...

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19. Norma receives $400,000 from a life insurance policy with which she purchases an annuity-certain. The annuity will pay 12 equal annual installments, with the first payment made immediately. On the day she receives payment number 6 she is offered, in lieu of the future annual payments, a new payment scheme: (i) 8 annual payments of $20,000, beginning in one year, followed by a monthly perpetuity of X. (ii) The first monthly perpetuity payment would occur one month after the last annual payment of $20,000. The effective annual rate of interest is 10% for the entire time period. Determine the value of X. [Hint: rearrange cash flow to form different annuities, also starting at different times] 19. Norma receives $400,000 from a life insurance policy with which she purchases an annuity-certain. The annuity will pay 12 equal annual installments, with the first payment made immediately. On the day she receives payment number 6 she is offered, in lieu of the future annual payments, a new payment scheme: (i) 8 annual payments of $20,000, beginning in one year, followed by a monthly perpetuity of X. (ii) The first monthly perpetuity payment would occur one month after the last annual payment of $20,000. The effective annual rate of interest is 10% for the entire time period. Determine the value of X. [Hint: rearrange cash flow to form different annuities, also starting at different times]