Question

You enter to play the lottery. To your surprise, you've won! You are given the option to accept either a lump-sum payment of $105 million today or annual lifetime payments of $3,582,000 beginning today. Assuming current rates of interest are at 3.25% which is the better decision. Be sure to discuss all the aspects and assumptions in making your decision and any calculations you have made to support that decision. How old would you have to live to be indifferent between the two choices?

Also, assuming you make $70,000 a year and want to replace 80% of your income in the case of your untimely death, given your current age and the expectation that you will need to cover your family for the loss of income until you retire at 70, how much life insurance do you need to do so? (Hint: consider the need to be the potential that you would die tomorrow and your policy would need to pay out $70,000 each year until you were to be 70.) Be sure to identify the method of calculation in your discussion and use a risk-free rate of investment of 3.25%.

Answer 1

The present value of the lump sum payment is 105 million

The present value of the annual lifetime payments = PMT / r where PMT is the annual payment and r is the interest rate

PV = 3,582,000 / 0.0325 = 110.215 million, so the annual lifetime payment is the better decision

PV = PMT x ((1 – (1 / (1 + r) ⁿ)) / r)

We have to find the value of 'n' for which PV = 105 million, PMT = 3.582 million and r = 3.25%

Solving the above equation we get n = 95.39 years

We have to find PV = PMT x ((1 – (1 / (1 + r) ⁿ)) / r), where PV is the insurance amount needed, PMT is the annual income that needs to be replaced and n is the number of years until you turn 70 (not given in the question)

PMT = 70,000 x 80% = 56,000

r = 3.25 %

n = 70 - 30 = 40 (lets assume you are 30 years old)

PV = $1,243,672.26