6. A lottery offers two options for the prize.

Option A: $1000 a week for life
Option B: $ 600 000 in one lump sum.

The current expected rate of return for large investment is 7%/a, compounded weekly.

a. Which option would the winner choose if s/he expects to live for another 25 years?

b. At what point in time is Option A better than Option B?

a. To determine which option the winner would choose, we need to calculate the present value of each option and compare them.

Option A provides $1000 a week for life, which is an annuity. The present value of an annuity can be calculated using the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r,

where PV is the present value, PMT is the weekly payment, r is the interest rate per period (in this case, the weekly compounded rate of 7%/52 = 0.1346%), and n is the number of periods (in this case, 25 years * 52 weeks/year = 1300 weeks).

Calculating the present value of Option A:
PV(A) = 1000 * (1 - (1 + 0.001346)^(-1300)) / 0.001346

Option B provides a lump sum of $600,000, which is already the present value.

Now we compare the present values:
If PV(A) > PV(B), the winner would choose Option A.
If PV(A) < PV(B), the winner would choose Option B.

b. To determine when is Option A better than Option B, we need to compare the present values of both options at different points in time.

For a specific point in time t, the present value of Option A would be:
PV(A, t) = PMT * (1 - (1 + r)^(-t)) / r,

where t is the number of weeks since winning the lottery.

We can compare PV(A, t) and PV(B) to find the point in time when Option A becomes better than Option B:
If PV(A, t) > PV(B), Option A is better.
If PV(A, t) < PV(B), Option B is better.

By comparing the present values at different points in time, we can determine when Option A becomes better than Option B.