Final answer:
David purchased a convertible term life insurance policy that allowed him to switch to a whole life policy with a cash value component without proof of insurability.
Step-by-step explanation:
David purchased a type of policy known as a convertible term life insurance. This policy allows the policyholder to convert from a term life insurance policy, which offers a death benefit for a specified term, to a whole life insurance policy, which provides a death benefit and also accumulates a cash value over time, without having to show proof of insurability. Whole life insurance serves as permanent life insurance with the added benefit of the cash value, which can be used as an account for the insured's use.