Question

The head of the household earns $150,000. You wish to insure against death. However you want to insure for the following: $75,000 protected for 30 years & $75,000 protected forever (infinitely). Assuming 2% inflation and 6% earnings rate determine the amount of insurance needed today

Answer 1

Answer-

Total earnings of head of houseold = $ 150000
Amount to be insured for 30 years = $ 75000
Amount to be insured forever ( infinitely) = $ 75000

Earnings rate = 6 %
Inflation rate = 2 %

When accounted for inflation the real earnings rate = r = 6 % - 2 % = 4 %
Discount rate = ( 1+ 4 %) = (1+0.04) = 1.04

1ST Case

Amount insured for 30 years today = $ 75000 / ( 1+r)30  [ Present value calculation ]  

Amount insured for 30 years today = $ 75000 / (1.04)30

Amount insured for 30 years today = $ 75000 / 3.2434 = $ 23123.88

2ND Case

Amount insured for forever ( infinitely) = $ 75000

Let the Amount insured for forever (infinitely) today = $ P [ Present value ]

Therfore the amount at a rate of 4 % for infinity (perpetuity) = $ P / r = $ P / 0.04

Equating both the equations we get

$ P / 0.04 = $ 75000

$ P = $ 75000 x 0.04
$ P = $ 3000

Therefore the total amount needed for both insurances = $ 23123.88 + $ 3000 = $ 26123.88

The amount of insurance needed to day = $ 26123.88