You are looking to purchase a 25 year life insurance policy for $500,000

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You are looking to purchase a 25 year life insurance policy for $500,000. The policy will pay annually at the end of the year. The current market interest rate is 2.5%. What should the annual payment per year be? 2. You have earned a pension worth $2,000 a month and it pays at the beginning of the month, you think you will live and additional 15 years. The current prevailing interest rate is 2% per year. What is the current market value of your pension? 3. You are attempting to price a 25 year annuity due for your insurance company. Payments of $3,500 for this annuity due start at the beginning of each year. The investment team at your company guarantees a return of 8%. What is the lowest price your company should offer? 4. You start an annuity with $1 million and expect to receive 12 equal payments beginning at the end of the first year. The guaranteed annual interest rate is 6 percent. The annual payments that you expect to collect are? Name: 5. Calculate the annual cash flows of a $2 million, 10-year fixed-payment annuity due earning a guaranteed 8 percent annually if the payments are to start at the beginning of this year. 6. Calculate the college fund required to start a four year college program in 15 years time. The tuition fees are currently 15,000 and are first payable at the start of year 16. Inflation is 4% and the rate of return is 9%. You have currently saved nothing, What amount do you need to save at the end of each year to afford college tuition. 7. Mega Millions has reached a record-breaking jackpot of $1.6 billion. Whoever holds the winning lottery ticket will be given two options: They can collect their winnings as a one-time lump sum that's less than the value of the total jackpot in this case, and the lump sum payment would be $904,900,000, or they can receive the full amount in annual installments stretched out over 30 years. The annuity will pay out the equivalent value of the lottery 1.6 billion dollars (meaning the present value of all future cashflows). The lottery will guarantee a return of 5%. What would be the value of the annuity payments? If you were to take the lump sum payment what rate of return would make you indifferent between the annuity and the lump sum payment? 8. You are looking to invest $2million dollars in a deferred annuity. Calculate the annual cash flows of a $2 million, 10-year fixed-payment deferred annuity earning a guaranteed 8 percent per year if annual payments are to begin at the end of the sixth (6th) year. 1. Suppose you have just won the first prize in a lottery. The lottery offers you two possibilities for receiving your prize. The first possibility is to receive a payment of $10,000 at the end of the year, and then, for the next 15 years this payment will be repeated, but it will grow at a rate of 5%. The interest rate is 12% during the entire period. The second possibility is to receive $100,000 right now. Which of the two possibilities would you take? Answer: You want to compare the PV of the growing annuity to the PV of receiving $100,000 right now (which is, obviously just $100,000). So, here are the numbers: C = $10,000r = 0.12g = 0.05t = 16 PV = 10,000 [(1/0.07) - (1/0.07)*(1.05/1.12)16] = $91,989.41 < $100,000, therefore, you would prefer to be paid out right now. 2. You are looking to purchase a 25 year life insurance policy for $500,000. The policy will pay annually at the end of the year. The current market interest rate is 2.5%. What should the annual payment per year be? Annuity Payment = PV / [(1-(1+r)-n)/r] PV - present value r - rate of return n - number of periods Annuity Payment = 150,000/[(1-(1+0.025)-25)/0.025] = 150,000/[0.46/.025] = 150,000/18.42 = $8,141.39 The annual payment for the insurance policy will be per year will be $8,141.39