• 3(a) Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9).

• What is the duration of the pension obligation? The current interest rate is 10% per year for all maturities.

(3 marks)

(3)(b)Togeneratethescheduledpensionpayments,thepensionfundwantstoinvestthepresentvalueofthefuturepayoutsinbondsandmatchthedurationofitsobligationinparta).Ifthefunduses5-yearand10-yearzero-couponbondstoconstructitsinvestmentposition,howmuchmoney(dollaramount)oughttobeplacedineachbondnow?Whatshouldbethetotalfacevalue(notcurrentmarketvalue)ofeachzero-couponbondheld?(3)(c) Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 10% p.a.to 9% p.a. Show that the investment position constructed in part b) can still fund (approximately) the future payments by showing that the funds net investment is close to 0 at the end of year 9 after making all the scheduled payments. Assume that interest rates will remain at 9% p.a. Any excess cash from the 5-year investment will be reinvested at 9% and any fraction of the 10-year bonds held can be sold at the going market price at any time to fund the annual payments.

(6 marks)

(Total for Question: 12 marks)

What is the answer of 3 C??? how to solve 3(c)?