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Annuities Practice Problems
Prepared by Pamela Peterson Drake
0. 0. Congrats! You just won the $64 million Florida lottery. Now the Surely Company is offering you $30 million in exchange for the 20 installments on your winnings. If your opportunity cost of funds is 8%, should you agree to this deal? 0. Given: CF = $64,000,000 / 20 = $3,200,000 N = 20 i = 8% Annuity due PV = $33,931,517.44 No: the annuity is worth almost $34 million to you, but Surely is offering only $30. 0. Carol Calc plans on retiring on her 60th birthday. She wants to put the same amount of funds aside each year for the next twenty years -- starting next year -- so that she will be able to withdraw $50,000 per year for twenty years once she retires, with the first withdrawal on her 61st birthday. Carol is 20 years old today. How much must she set aside each year for her retirement if she can earn 10% on her funds? 0. PV60 = $50,000 (PV annuity factor for N=20, i=10%) PV60 = $50,000 (8.5136) PV60 = $425,678.19 Because she will stop making payments on her 40th birthday (first is on her 21st birthday, last is on her 40th birthday), we must calculate the balance in the account on her 40th birthday: PV40 = PV60 / (1 + 0.10)20 = $63,274.35 Then, we need to calculate the deposits necessary to reach the goal: FV40 = PV40 = $63,274.35 N = 20 i = 10% FV = CF (FV annuity factor for N=20, i=10%) $63,274.35 = CF (FV annuity factor for N=20, i=10%) $63,274.35 = CF (57.2750) CF =payment = $1,104.75 per year 0. Have I got a deal for you! If you lend me $100,000 today, I promise to pay you back in twenty-five annual installments of $5,000, starting five years from today (that is, my first payment to you is five years from today). You can earn 6% on your investments. Will you lend me the money? 0. This is a deferred annuity problem CF = $5,000 N = 25 i = 6% PV4 = $5,000 (PV annuity factor for N=25 and i=6%) PV4 = $5,000 (12.7834) PV4 = $63,916.78 PV0 =
Prepared by Pamela Peterson Drake
0. 0. Congrats! You just won the $64 million Florida lottery. Now the Surely Company is offering you $30 million in exchange for the 20 installments on your winnings. If your opportunity cost of funds is 8%, should you agree to this deal? 0. Given: CF = $64,000,000 / 20 = $3,200,000 N = 20 i = 8% Annuity due PV = $33,931,517.44 No: the annuity is worth almost $34 million to you, but Surely is offering only $30. 0. Carol Calc plans on retiring on her 60th birthday. She wants to put the same amount of funds aside each year for the next twenty years -- starting next year -- so that she will be able to withdraw $50,000 per year for twenty years once she retires, with the first withdrawal on her 61st birthday. Carol is 20 years old today. How much must she set aside each year for her retirement if she can earn 10% on her funds? 0. PV60 = $50,000 (PV annuity factor for N=20, i=10%) PV60 = $50,000 (8.5136) PV60 = $425,678.19 Because she will stop making payments on her 40th birthday (first is on her 21st birthday, last is on her 40th birthday), we must calculate the balance in the account on her 40th birthday: PV40 = PV60 / (1 + 0.10)20 = $63,274.35 Then, we need to calculate the deposits necessary to reach the goal: FV40 = PV40 = $63,274.35 N = 20 i = 10% FV = CF (FV annuity factor for N=20, i=10%) $63,274.35 = CF (FV annuity factor for N=20, i=10%) $63,274.35 = CF (57.2750) CF =payment = $1,104.75 per year 0. Have I got a deal for you! If you lend me $100,000 today, I promise to pay you back in twenty-five annual installments of $5,000, starting five years from today (that is, my first payment to you is five years from today). You can earn 6% on your investments. Will you lend me the money? 0. This is a deferred annuity problem CF = $5,000 N = 25 i = 6% PV4 = $5,000 (PV annuity factor for N=25 and i=6%) PV4 = $5,000 (12.7834) PV4 = $63,916.78 PV0 =