Question

Assume that Social Security promises you $ 41,000 per year starting when you retire 45 years from today​ (the first $ 41,000 will get paid 45 years from​ now). If your discount rate is 9 %​, compounded​ annually, and you plan to live for 18 years after retiring​ (so that you will receive a total of 19 payments including the first​ one), what is the value today of Social​ Security's promise?

Answer 1

PV= $7593.12

Step-by-step explanation:

Giving the following information:

We have 19 equal payments of $41,000 at a rate of 9 %​, compounded​ annually. We need to find the present value.

First, we need to calculate the final value with the following formula:

FV= {A*[(1+i)^n-1]}/i

A= annual deposit

FV= {41,000*[[1.09^19)-1]}/0.09= $1,886,756.79

Now, we can calculate the present value:

PV= FV/(1+i)^n

PV= 1886756.79/1.09^64= $7593.12