Question

Assume that Social Security promises you $50,000 per year starting when you retire 45 years from today (the first $50,000 will get paid 45 years from now). If your discount rate is 4%, compounded annually, and you plan to live for 17 years after retiring (so that you will receive a total of 18 payments including the first one), what is the value today of Social Security's promise? g

Answer 1

$112,697

Step-by-step explanation:

The deferred annuity can be calculated in two steps:

Step 1: Calculate the annuity by using the following formula:

Value of Annuity at the year 44 = Annuity Payment * Annuity Factor

Here

Annuity Payment is $50,000

Annuity Factor = (1 - (1 + r)^-n) / r

n is 18 year from year 44 to year 62

r is 4%

So

Annuity Factor = (1 - (1 + 4%)^-18) / 4%

= 12.659

By putting values, we have:

Value of Annuity at the year 44 = $50,000 * 12.659

Value of annuity in year 44 = $632,965

Step 2: Discount it back to year zero

Present value today = $632,965 / (1.04)^44

Present value today = $112,697