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

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

Step-by-step 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)=(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)=(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=(FutureValue)/((1+r)^(n) )`

That is:

`PresentValue=(373,423.77)/((1+0.09)^(45) ) =7,726.98`

Best of luck.