A life insurer owes $550,000 in eight years. To fund this outflow,the insurer wishes to buy STRIPS that mature in eight years. The STRIPS have a $5,000 face value per STRIP and pay a 6 percent APR with semiannual compounding. How much must the insurer spend now to fully fund the outflow (to the nearest dollar)?

Question

Quizplus · Accepted Answer

To fully fund the outflow, the insurer needs to calculate the present value of the $550,000 that is due in eight years using the given 6 percent APR with semiannual compounding. The formula for the present value (PV) is PV = FV / (1 + r/n)^(nt), where FV is the future value ($550,000), r is the annual interest rate (0.06), n is the number of compounding periods per year (2 for semiannual), and t is the time in years (8). Plugging these values into the formula gives PV = $550,000 / (1 + 0.06/2)^(2*8) = $550,000 / (1.03)^16 ≈ $342,742. This is the amount the insurer must spend now to fully fund the $550,000 outflow in eight years.

A Life Insurer Owes $550,000 in Eight Years