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)

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.

Answer 3

To calculate the amount of life insurance you should purchase, you need to consider the future value of $58,000 at a 3% inflation rate for 20 years.

Step 1: Calculate the future value of $58,000 after 20 years of inflation:
Using the formula for future value (FV) of a present value (PV) compounded annually, we can calculate the future value of $58,000 after 20 years with a 3% inflation rate.
FV = PV * (1 + r)^n
where FV is the future value, PV is the present value, r is the interest rate (in this case, inflation rate), and n is the number of years.

FV = $58,000 * (1 + 0.03)^20
FV = $58,000 * (1.03)^20
FV = $58,000 * 1.806111
FV ≈ $104,676.78

Step 2: Calculate the life insurance needed:
Now that we have the future value of $58,000 after 20 years, we need to determine the life insurance amount to cover this future value.
The life insurance amount needed is equivalent to the future value of $104,676.78.

Therefore, you should purchase a life insurance policy that provides coverage of approximately $104,676.78 to replace $58,000 of your annual income until your child turns 20 years old, assuming a 3% inflation rate.