Assume that Social Security promises you $40,000 per year starting when you retire 45 years from...
Question:
Assume that Social Security promises you $40,000 per year starting when you retire 45 years from today (the first $40,000 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?
Discount Rate:
Discount Rate is the rate at which short-term loans are provided by financial institutions. This rate is subject to change with the change in inflation. This rate is used to calculate the present value of future cash inflows and outflows.
Answer and Explanation: 1
{eq}\begin{align*} {\rm\text{Amount to be received}} &= {\rm\text{Annual amount}} \times {\rm\text{PVAF}}(17{\rm\text{years}},7\% )\\ &= \$ 40,000 \times 9.763\\ &= \$ 390,520 \end{align*} {/eq}
{eq}\begin{align*} {\rm\text{Present Value Of Promise}} &= {\rm\text{Annual amount}} \times {\rm\text{PVAF}}(45{\rm\text{years}},7\% )\\ &= \$ 40,000 \times 13.606\\ &= \$ 544,240 \end{align*} {/eq}
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