Final answer:
The original loan amount General Motors borrowed was calculated using the simple interest formula. By knowing the total repayment of $82 million, an interest rate of 8%, and a time period of 1 year, we determined the original loan was approximately $75.93 million.
Step-by-step explanation:
The student is asking how to determine the original loan amount that General Motors had borrowed, given the total cost of repaying the loan and the interest rate. To calculate the original loan amount, also known as the principal, we use the formula for simple interest, which is Interest = Principal × Rate × Time. In the context of General Motors' scenario, the total repayment (which includes both the principal and the interest) is $82 million, the interest rate is 8% per year, and the time is 1 year.
Firstly, we convert the rate into decimal form by dividing it by 100, which gives us 0.08. Since the time is 1 year, we multiply the principal by 0.08 to find the interest for one year. We set up the equation $82 million = Principal + (Principal × 0.08 × 1) to find the original loan amount. When we solve for the principal, it turns out that General Motors' original loan was approximately $75.93 million. This type of mathematical problem demonstrates the practical applications of arithmetic and algebra in financial mathematics, particularly in the area of loans and interest calculations. Understanding how interest works and how it can dramatically affect the total amount repaid is essential when managing debts and planning financial obligations.