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)?

Respuesta :

Answer:

Today, the funder will invest 342,741.82 dollars

Explanation:

We invest on a lump sum of STRIPS which yield 6% with semiannual compounding.

Our target is 550,000 in eight years and each STRIPS is valued at 5,000

The STRIP is the coupon payment or maturity payment of a bond which sales like a zero coupon bond so we need to discount the 550,000 at the market rate to know the market price of the STRIPS:

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  $550,000

time   16.00 (8 years x 2 compounts per year)

rate  0.03 ( 6% annual divide into 2 to get semiannual rate)

[tex]\frac{550000}{(1 + 0.03)^{16} } = PV[/tex]  

PV   342,741.82