Consider a guaranteed annuity contract issued by a life insurance company with a rate of 3.08% and a term of 20 years. F

[answerhappygod]

Consider a guaranteed annuity contract issued by a lifeinsurance company with a rate of 3.08% and a term of 20 years. Fora $100,000 nominal amount, the insurance company is promising topay $183,437.53 (=100,000*(1.0308)^20) to the holder of theguaranteed annuity contract in 20 years. We want to know theinterest rate risk exposure to the company if it funds thisliability using a 30-year bond with a coupon rate of 3.08% issuedat par. To do so, assume that in the first year, rates change toone of the five possible values in row 18 and then stay constantfor the next 20 years. For each rate change, calculate two things:(1) the future value (as of 20 years down the road) of each couponpayment made by the 30-year bond for the next 20 years, and (2) thevalue at year 20 of the bond used to fund the obligation. For (1),assume the coupons are reinvested at the new prevailing interestrate. The sum of the reinvested coupons and the value of the bondare the total future value of the assets used to finance theannuity contract.
What is the duration of the annuitycontract?

Consider A Guaranteed Annuity Contract Issued By A Life Insurance Company With A Rate Of 3 08 And A Term Of 20 Years F 1 (77.85 KiB) Viewed 8 times

Reinvestment Risk Inputs Annual Coupon Rate (CR_P3) Yield to Maturity (Annualized) (YTM_P3) Number of Payments / Year (NOP_P3) Number of Periods to Maturity (T_P3) Face Value (M_P3) Maturity of Liability Calculations Discount Rate / Period (DR_P3) Coupon Payment (l_P3) Duration of bond Future value of annuity contract Duration of annuity contract Future value at time 20 of payment #: 1 2 3 4 5 6 u789 10 1112 131415 16 17 18 19 20 Value of Bond at Time 20 Total Value of Bond and Reinvested Proceeds at Time 20 3.08% 3.08% 1 30 100,000 20 3.08% #N/A #N/A #N/A Rates changes to: 4.00% 2.00% Displayed Formula for Year 1 Coupon FV: Displayed Formula for Bond Value at t=20: Displayed Formula for Total Value: Description of how value of reinvested coupons and value of the bond at t=20 changes with interest rates: 3.00% 3.20%