An insurer prices disability income insurance using the sickness-death model. The following prob- abilities apply for a healthy life aged 50: 1 00 -0.015t -0.01t tP50 3 -e 4 + 4 02 tP50 1-e-0.016 Policyholders pay premiums continuously throughout the policy term while they are healthy, and receive benefits while they are disabled. Policyholders are assumed to be healthy at the issue date. Consider a policy with term three years for a life aged 50 that provides a disability income benefit at the rate of $6000 per year. Using a force of interest of 5% per year, calculate (a) the EPV of the disability benefit. (b) the annual premium rate