4. An insurer is designing a 10-year single premium variable annuity policy with a guaranteed maturity benefit of 85% of the single premium. (a) Calculate the value of the GMMB at the issue date for a single premium of $100. (b) Calculate the value of the GMMB two years after issue, assuming that the policy is still in force, and that the underlying stock prices have decreased by 5% since inception. Basis and policy information: Age at issue: 60 Front end expense loading: 2% Annual management charge: 2% at each year end (including the first) Survival model: Standard Ultimate Survival Model Lapses: 5% at each year end except the final year Risk-free rate: 4% per year, continuously compounded Volatility: 20% per year. 4. An insurer is designing a 10-year single premium variable annuity policy with a guaranteed maturity benefit of 85% of the single premium. (a) Calculate the value of the GMMB at the issue date for a single premium of $100. (b) Calculate the value of the GMMB two years after issue, assuming that the policy is still in force, and that the underlying stock prices have decreased by 5% since inception. Basis and policy information: Age at issue: 60 Front end expense loading: 2% Annual management charge: 2% at each year end (including the first) Survival model: Standard Ultimate Survival Model Lapses: 5% at each year end except the final year Risk-free rate: 4% per year, continuously compounded Volatility: 20% per year