Question

John is the beneficiary of a life insurance policy. The insurance company informs John that he has two options for receiving the insurance proceeds. He can retrieve a lump sum of $125,000 today or receive payments of $4,000 a month for forty months. He can earn 12% per year on his money. Which option would you take ?

Answer 1

Select the option with higher PV.

PV of $ 125000 today is $ 125000

PV of $ 4000 for 40 Months:

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

Particulars	Amount
Cash Flow	$            4,000.00
Int Rate	1.0000%
Periods	40

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 4000 * [ 1 - [(1+0.01)^-40]] /0.01
= $ 4000 * [ 1 - [(1.01)^-40]] /0.01
= $ 4000 * [ 1 - [0.6717]] /0.01
= $ 4000 * [0.3283]] /0.01
= $ 131338.74

As $ 4000 for 40 Months having higher PV, It will be selected.