Final answer:
The present value of Social Security's promise of $30,000 annually starting 45 years from today for 19 payments at a discount rate of 6% is calculated using the formula for the present value of an annuity due. Each payment is discounted to today's value, considering the initial 45-year delay before the first payment is received.
Step-by-step explanation:
The value today of Social Security's promise of $30,000 per year, starting 45 years from now and lasting for 19 payments, can be calculated using the present value formula for an annuity. This involves discounting each of the 19 payments back to the present at the discount rate of 6%. To solve for the present value, we use the formula for the present value of an annuity due, which accounts for the first payment occurring immediately after retirement:
Present Value = Payment × ((1 - (1 + r)^-n) / r), where 'Payment' is the annual payment received, 'r' is the discount rate, and 'n' is the total number of payments.
Given that the first payment will be made 45 years from today, we have to account for that delay by discounting the entire value of the annuity back an additional 45 years at the rate of 6%. Therefore, we calculate the present value of the annuity and then discount that sum back to present value using the formula P = P' / (1+r)^t, where 'P' is the present value we're solving for, 'P'' is the present value of the annuity as calculated above, 'r' is the discount rate, and 't' is the number of years until the first payment.
It's important to remember that calculations like this are based on assumptions about rates of return and longevity, and actual future values may vary due to economic conditions and changes to the Social Security program.