Question

An insurance company offers a $120,000 term life policy lasting 2 years to a man of average health aged 50. To value the policy, the company has four conditions: (1) the yearly interest or discount rate is 4%, (2) the compounding or discounting is done every 6 months, (3) the premium is made once at the start of a year, and (4) the payout occurs at the end of a year. What is the company’s break-even yearly premium?

Answer 1

Answer :-

Calculation of Break- Even Yearly Premuin by insurance company if :-

Maturity Value after 2 years = $120,000

Interest Rate = 4%

Compounding is done at every 6 months and premium is paid at the starting of the year ,

Formula to Determine Present of annuity is :-

P = PMT x ((1 – (1 / (1 + r) ^ -n)) / r)

where

P = the present value of annuity ($120000 )

PMT = the amount in each annuity payment (Premium)

R= the interest or discount rate(4%) = But since it is compounding in every 6 months therefore rate( 4%*6/12) = 2%

n= the number of payments left to receive = 2 Years

TO Find :- Break even Premium Amount

Maturity amount = Yearly Premium x ((1 – (1 / (1 + r) ^ -n)) / r)

120000 = Premium x ((1 – (1 / (1 + 0.02) ^ -2)) / 0.02)

Premium = $80,000

Therefore  company’s break-even yearly premium is $80,000