Spring 2019 FIN 6102

Please complete the following problems. Each problem is worth 5 points each. Maximum number of points available is 40.

1. You are looking to purchase a 25 year life insurance policy for $150,000. 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, 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?

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 12,000 and are first payable at the start of year 16. Inflation is 4% and the rate of return is 9%. Calculate the lump sum which needs to be invested today to provide the college fund.

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, it would be $904,900,000, or they can receive the full amount in annual installments stretched out over 29 years. The annuity will pay out 1 billion dollars (meaning the present value of all future cashflows). The current inflation rate is 3%. What interest rate would make you indifferent between the annuity and the lump sum payment?

8. 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.