Question

Robert is considering a 20-year renewable term insurance policy, with a face vale of $500,000 for a $400 yearly premium. However, his insurance agent told him of a new option where he can receive his accumulative premium payments ($400 a year for 20 years) at the end of the policy. This feature will change the yearly premium from $400 to $650. Should Robert accept this option if his after-tax rate of return is 4.56%? (Note: His insurance agent reminded him that nearly 98% of all term policies are never paid out, so this will allow him the protection and receive a lump sum at the end of the policy, if he is still living, of $8,000)

Answer 1

Annual insurance premium = $400

Annual premium payable in the alternate option = $650

Hence, extra $250 has to be paid for 20 years in the alternate option.

This extra $250 per year if invested else where, can earn interest 4.56% per year. Since premium is paid at the begining of every year, hence $250 invested annually for 20 years will become equal to the following:

Future value = A(1 + r)[{(1+ r)ⁿ - 1}/r

where, A = Annuity amount

r = Annual interest rate

n = Number of years

Future value = 250 (1 + 0.0456)[(1 + 0.0456)²⁰ - 1]/0.0456

= 250 (1.0456){[(1.0456)²⁰ - 1]/0.0456}

= 261.4 [2.43956]/0.0456

= 261.4 x 53.49912

= $13,985

Hence, if $250 are invested annually at the begining of every year for 20 years at 4.56% interest, it will amount to $13,985. Hence, Robert should not accept the option of paying annually $650 premium. He should accept the insurance plan of paying premium of $400 annually and invest remaining $250 elsewhere.