Eternal Life Insurance - Fair Deal Premium Calculation

Fair Deal Premium Calculation

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Question

Eternal Life Insurance has a policy that will pay $50,000 per year starting 20 years from now, to you and all your progeny. If the appropriate discount rate is 10% per year and you have to pay premiums every year for the next 15 years starting at the end of this year, what's the annual premium payment that you and your heirs must make for this to be a fair deal?

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A

You are entitled to a perpetuity which start paying 20 years from now. Therefore, at the end of year 19, you will have an asset worth $50,000/0.1 = $500,000. The present value of this equals $500,000/1.1^19 = $81,754. Your premium payments are a 15-year annuity. If the annual premium is P, then this annuity has a present value of P/0.1*[1 - 1/1.1^15] = 7.606P. This must equal the value of the perpetuity for this to be a fair deal. This gives P = $81,754/7.606 = $10,749.