Question

You just paid $750,000 for an annuity that will pay you and your heirs $45,000 a year forever. What rate of return are you earning on this policy?

Answer 1

5.25 %

Answer 2

$750,000*x/100=$45,000
x=6%

Answer 3

The longer the annuity pays out (in most cases the longer you live), the closer the rate of return gets to 45000/750000 = 0.06

Since this one keeps going forever, the rate will just be 0.06 or 6%

Here is the math:

A = P/r*[1-(1+r)^-t]
as t goes to infinity, (1+r)^-t goes to 0, so the whole expression becomes:
A=P/r
That allows us to solve for r:
r = P/A

In this case:
r = 45000/750000 = 0.06 or 6%