The right of a title company to receive any damages available to the insured when the title company has made a payment to settle a claim covered by a policy is called

The correct answer is letter "B": subrogation.

Explanation:

Subrogation describes the right an insurance company has to ask for a refund of the expenses of the coverage of insurance to a third party -typically another insurance- that is also involved in an unfortunate event from where the insured was harmed.  

Usually, the subrogating insurance prefers to take charge of the expenses to provide the insured immediate assistance but, after realizing the liability implied by the third party, the subrogating insurance requests a reimbursement. Subrogation is mostly applied to auto, healthcare and home insurance.

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20