each of each year for eighteen yeals. t pur of each year for twenty years, then paymets fhents annual effective discount rate of 10%. Find Q. pOr payments of SQ at the and Y are equal when calculated e thereafter. The present values of X and Y are using an day she was bom received a gift of a twenty-one year annuity on the The annuity pays $500 on her odd birthdays and $700 (a) If the nominal rate of interest is 8% payable (7) Lucy even birthday find the value of this annuity on the day she was born. $6,000, find the the nearest one- (b) If the value of the annuity at the time of her birth was S annual effective discount rate as a percent, correct to hundredth of a percent. (8) On January 1, Alex received an inheritance of a thirty-year ann each April 1, $1,500 each July 1, and $3,000 each October 1 annuity. Startin on the day of the inheritance, the annuity pays $1,000 each Janutartng on the day Alex y nay 1,s2.000 inherits it. (b) If the value on the day she inherits it is $130,000, find the annual effecti ve rate i used to calculate this value to the nearest hundredth of a percent (3.8) Annuities with payments in geometric progressions (1) Al and Sal are twins. Al is given a fifteen-year annuity with end-of-year pay ments. The first payment Al receives, precisely one year from the date he is given the annuity, is for $100, and then subsequent payments decrease by 4% annually. Sal is given an n-year level annuity that has the same present value as Al's when the present values are calculated using i = 5%. Again calculated using i 5%, the accumulated value at the end of n years of Sal's annuity is $1,626.29. Find the common present value of the two annuities and then find n (2) On January 1, 1988, Wanda received a deferred perpetuity paying $3,000 uly 1 of even numbered years beginning on July 1, 1996 and $1,200 on July 1 of odd years beginning on July 1, 1997. The interest rate is 4% effective for even numbered years and 5% effective for odd numbered years the interest rate is 4% effective for 1988, 1990, 1992, and 5% effect 1989,1991, 1993,... Find the value of this perpetuity on January 1, 1988 ve for (3) Consider an annuity-immediate with monthly payments for twenty years payments are level in the course of each year, then increase by 2% for the nex