Question

Your first baby was born yesterday and is healthy and strong. To guard against your premature death, you want to purchase a life insurance policy that will replace $58,000 of your annual income until your child is 20 years old. How much life insurance should you purchase, if you assume a 3% inflation rate? (Do NOT worry about Social Security for this example)

Answer 1

well, say we have the present value of an annuity. Usually the value goes up at interest rate r but in this case we have only inflation, negative interest (unrealistic of course, presumably your successor would deposit the insurance proceeds in an interest bearing account, hopefully at least 3%.)
Therefore I will use r = -.03

P= 58,000 [ 1 -(1-.03)^-20]/-.03

= 58,000 [ -.83893]/-.03

= 58,000 [ 27.96 ]

= 1,621,932.29

instead of 58,000*20 = 1,160,000

Answer 2

By the way, die right away to get the maximum if it stops at age 20. Best make it for 20 years after you die.