Final answer:
Bank A with semi-annual compounding is generally a better choice than Bank B with quarterly compounding for an auto loan because it will have a lower effective interest rate, leading to less interest paid over the life of the loan.
Step-by-step explanation:
The student's question is concerning the comparison of auto loans from two banks with different compound interest frequencies. The main answer is that Bank A, which offers semi-annual compounding, would generally be a better choice compared to Bank B that offers quarterly compounding. This is because the more frequent the compounding, the higher the amount of interest that will accumulate over time. Despite the same nominal interest rate of 5%, these banks do not offer the same effective interest rate due to their differing compounding frequencies.An explanation for this can be illustrated through the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), t is the time the money is invested for, and n is the number of times that interest is compounded per year. When you calculate the effective interest rate for each bank (taking into account the different compounding periods), you will find that Bank B's effective interest rate is slightly higher than 5%, thus increasing the cost of the loan over time.In conclusion, when comparing auto loans with different compounding frequencies but the same nominal rates, you should look for the one with less frequent compounding to minimize the total interest paid.