Question

Assume that Social Security promises you $45,000 per year starting when you retire 45 years from today? (the first $45,000 will get paid 45 years from? now). If your discount rate is 7 % 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?

Answer 1

To calculate the present value of Social Security's promise, we use the annuity present value formula with a 7% discount rate, and discount 18 annual payments of $45,000 each back to today's dollars, taking into account that the first payment will be made 45 years in the future.

Step-by-step explanation:

The question asks us to determine the present value of a series of future Social Security payments, given a discount rate of 7% compounded annually. To find the present value of these payments, we use the present value formula for an annuity, which accounts for the compounding effect over time. The payments are expected to be $45,000 per year for 18 years, starting 45 years from now. We discount each payment back to the present value and sum them up to find the total present value of the annuity. In this case, the formula includes discounting 45 years for the first payment and 1 less year for each subsequent payment until the last payment is discounted back 45-17=28 years.