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this is an actuarial science question. 6. You are given the following Disability Income...

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this is an actuarial science question.

6. You are given the following Disability Income Model to price a 10 -year insurance policy issued to (x) : The product has the following features. (i) Policyholders are healthy at the issue date. (ii) A benefit of 15,000 is payable immediately on death within 10 years. (iii) A continuous benefit of 1000 per year is paid while the policyholder is in the Sick state, during the 10-year term. (iv) Premiums are payable continuously while the life is in the Healthy state. (v) Maintenance expenses are paid at a continuous rate of 50 per year while the insured is alive. (vi) Commissions are payable continuously at a rate of 7% of gross premium. (vii) No benefits, premiums or expenses are payable beyond 10 years. You are also given =6%,x+t01=0.02,x+t02=0.01,x+t10=0.005,x+t12=0.05, and ax:1000=5.144,ax:1001= 0.654,Ax:1001=0.165,Ax:1002=0.131. (a) Determine the gross premium rate by using the equivalence principle. You should calculate the value to the nearest 0.1 . (b) Calculate the probability that the life dies via becoming sick, within the 10 -year term

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