Question

Andrew decides to wait until age 65 to begin receiving social security benefits. find the present value of his estimated $26,000 per year in payment assuming 6% per year and payment until his 90th birthday.

Answer 1

We can solve this problem by using the formula for finding the present value given the annuity values. The formula is given as:

P = A * [(1 + i)^n – 1] / i (1 + i)^n

Where,

P = present value of the annuity

A = the annuity value = $26,000

i = interest rate = 0.06

n = number of years = 90 – 65 = 25

Substituting the given values to the equation:

P = 26,000 * [(1 + 0.06)^25 – 1] / 0.06 (1 + 0.06)^25

P = 26,000 * 12.783356183

P = $332,367.26

Therefore the present value of his social security benefits will be about $332,367.26