Assume that at retirement you have accumulated $500,000 in a variable annuity contract. The assumed investment return is 6%, and your life expectancy is 15 years. What is the hypothetical constant-benefit payment?

The hypothetical constant-benefit payment is $51,481.38.

Explanation:

This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * [{1 - [1 / (1 + r)]^n} / r] …………………………………. (1)

Where;

PV = Present value accumulated retirement benefit = $500,000

P = Annual hypothetical constant-benefit payment = ?

r = investment return = 6%, or 0.06

n = life expectancy = 15

Substitute the values into equation (1) and solve for P, we have:

$500,000 = P * [{1 - [1 / (1 + 0.06)]^15} / 0.06]

$500,000 = P * [{1 - [1 / 1.06]^15} / 0.06]

$500,000 = P * 9.712248987741

P = $500,000 / 9.712248987741

P = $51,481.38

Therefore, the hypothetical constant-benefit payment is $51,481.38.