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You have just won the lottery and you can choose between thefollowing payout options. The annual interest rate (EAR) is 10%. a)$100,000 right now and $60,000 every two years starting 3 yearsfrom now and ending 17 years from now (i.e., payments are at t = 0,t = 3, t = 5, … , t = 15, t = 17). b) $60,000 a year for 25 yearswith the first payment one year from today (i.e., payments are at t= 1, 2, … 24, 25). c) 25 annual payments of $45,000 and a 26thpayment of $299,000. The first payment is made right now, and the$299,000 payment is made one year after the last $45,000 payment.How much more is the best option worth today relative to the worstoption?

Select one:

a. $920,000

b. $276,678

c. $241,409

d. $221,088

e. $235,871

f. $191,898

g. $235,323

h. -$67,712

NOTE: Please show all the work, not using EXCEL. (Step by stepwith equations) Thanks!

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Irving Heathcote
Irving HeathcoteLv2
28 Sep 2019

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ou have just won the lottery and you can choose between the following payout options. The annual interest rate (EAR) is 10%.

a) $100,000 right now and $60,000 every two years starting 3 years from now and ending 17 years from now (i.e., payments are at t = 0, t = 3, t = 5, ... , t = 15, t = 17).

b) $60,000 a year for 25 years with the first payment one year from today (i.e., payments ar e at t = 1, 2, 3 ... 24, 25).

c) 25 annual payments of $45,000 and a 26th payment of $299,000. The first payment is made right now, and the $299,000 payment is made one year after the last $45,000 payment. How much more is the best option worth today relative to the worst option?

Assume that your father is now 50 years old, plans to retire in10 years, and expects to live for 25 years after he retires - thatis, until age 85. He wants his first retirement payment to have thesame purchasing power at the time he retires as $50,000 has today.He wants all of his subsequent retirement payments to be equal tohis first retirement payment. (Do not let the retirement paymentsgrow with inflation: Your father realizes that if inflation occursthe real value of his retirement income will decline year by yearafter he retires). His retirement income will begin the day heretires, 10 years from today, and he will then receive 24additional annual payments. Inflation is expected to be 6% per yearfrom today forward. He currently has $100,000 saved and expects toearn a return on his savings of 7% per year with annualcompounding. To the nearest dollar, how much must he save duringeach of the next 10 years (with equal deposits being made at theend of each year, beginning a year from today) to meet hisretirement goal? (Note: Neither the amount he saves nor the amounthe withdraws upon retirement is a growing annuity.)

His recently departed Uncle Jimmy, may he rest in peace, hasleft Scott a 15-year annuity (15 annual payments). He will receivethe first payment of $8,000 in 5 years from today, and paymentswill grow at a constant rate of 3% per year thereafter. If he isdiscounting at 6% (EAR), what is the present value of hisinheritance?

Select one:

a. $73,911

b. $93,311

c. $69,727

d. $61,544

e. $127,530

f. $69,911

g. $98,909

h. No solution since r>g

NOTE: Please show all the work, without using EXCEL (Step bystep with equations) Thanks!

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