Question

Assume that Social Security promises you $ 44,000 per year starting when you retire 45 years from today​ (the first $ 44,000 will get paid 45 years from​ now). If your discount rate is 9 %​, compounded​ annually, and you plan to live for 13 years after retiring​ (so that you will receive a total of 14 payments including the first​ one), what is the value today of Social​ Security's promise?

Answer 1

Answer:

Ans. The value today of Social​ Security's promise is $7,726.98

Explanation:

Hi, well, first we need to bring to year 45 all 14 cash flows, and when they are at year 45, we have to bring it to present value, discounted at 9% rate, or 0.09.

First, let´s bring to year 45 all 14 future cash flows, the formula to use is the following.

$Value(yr-45)=\frac{A((1+r)^{n-1}-1) }{r(1+r)^{n-1} } +A$

That is because the first annuity is received exactly in year 45, it should look like this.

$Value(yr-45)=\frac{44,000((1+0.09)^{13}-1) }{0.09(1+0.09)^{13} } +44,000= 373,423.77$

Now we need to bring this to present value to asses the value today of Social​ Security's promise. For that, we use the following formula.

$PresentValue=\frac{FutureValue}{(1+r)^{n} }$

That is:

$PresentValue=\frac{373,423.77}{(1+0.09)^{45} } =7,726.98$

Best of luck.