Final answer:
The convexity of a loan on January 1, 2012, when Gary borrowed money to purchase a car, cannot be accurately determined from the given information as the question contains ambiguities and possible typos. Convexity is a measure of the sensitivity of the duration of a loan to changes in interest rates and is calculated using present values of cash flows. More specific information is needed to provide the correct expression for Gary's loan convexity. option c.
Step-by-step explanation:
The question is concerned with finding the correct expression for the convexity of a loan on which Gary borrowed money to purchase a car, with the first of 20 equal annual payments due immediately. The convexity of a loan is a measure of the sensitivity of the duration of a loan to changes in interest rates. The convexity is usually analyzed in financial mathematics to understand the interest rate risk of fixed income securities. While the provided information and expressions seem ambiguous and possibly contain clerical typos, generally the convexity can be calculated using the sum of the present values of cash flows, weighted by the time in years squared, and then adjusted for the price of the bond and the yield to maturity (YTM). However, without accurate formula options or payment amounts, it is not possible to confirm a correct expression for the convexity of the loan. The provided examples are related to different loan calculations and do not directly address the question of convexity of Gary's auto loan.