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?

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1 April, 09:42

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?

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Brennen Skinner · Answer 1

PV = $7593.12

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