Suppose you have just won the lottery and must choose one of the following riskless payoffs

Part A:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Present Value = Future Value / ( 1 + r )^n
= $ 140000 / ( 1 + 0.05 ) ^ 5
= $ 140000 / ( 1.05 ) ^ 5
= $ 140000 / 1.2763
= $ 109693.66

Part B:

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period.
PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 15000 * [ 1 - [(1+0.05)^-15]] /0.05
= $ 15000 * [ 1 - [(1.05)^-15]] /0.05
= $ 15000 * [ 1 - [0.481]] /0.05
= $ 15000 * [0.519]] /0.05
= $ 155694.87

Part C:

Present Value = Future Value / ( 1 + r )^n
= $ 120000 / ( 1 + 0.05 ) ^ 2
= $ 120000 / ( 1.05 ) ^ 2
= $ 120000 / 1.1025
= $ 108843.54

Part D:

Present Value = Cash flow / Disc Rate

= $ 7000 / 5%

= $ 140000

Option 2 has higher present value.