Final answer:
The loan payment situation described is an example of exponential growth due to the monthly compounded interest. Compound interest involves the growth of the loan balance over time, resulting in exponential growth. The loan balance can be calculated using the compound interest formula.
Step-by-step explanation:
The loan payment situation described in the question is an example of exponential growth rather than linear growth. This is because the loan includes an annual interest rate compounded monthly. Compound interest involves the growth of the loan balance over time, as each month the interest is added to the previous balance and contributes to the growth. This results in exponential growth of the loan balance.
To calculate the loan balance over time, you can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final loan balance
P = the principal loan amount (in this case, $400)
r = the annual interest rate (in this case, 8%)
n = the number of times interest is compounded per year (in this case, 12)
t = the number of years the loan is held for (in this case, the specific number of years is not provided)
Using this formula, you can calculate the loan balance over time and see that it grows exponentially due to the monthly compounding interest.