To decide which bank to choose for the loan, the effective interest rates must be calculated considering the compounding frequency. For Bank One with 7.1% compounded monthly and Bank Two with 7.375% compounded annually, the effective rates are different. By comparing these rates, we can determine which bank offers the lower rate and, therefore, represents the better deal.
The question is asking to compare the effective interest rates of two loans offered by different banks to determine which is more advantageous for a borrower. To calculate the effective interest rate, we need to account for the impact of compounding.
First, let's compute the effective interest rate for Bank One, which offers a nominal rate of 7.1% compounded monthly. The formula for the effective rate (ER) is ER = (1 + i/n)n - 1, where i is the nominal rate and n is the number of compounding periods per year. For Bank One, the effective rate can be calculated as:
ER Bank One = (1 + 0.071/12)12 - 1 = 1.005916712 - 1
For Bank Two, which offers a nominal rate of 7.375% compounded annually, the effective rate is simply the nominal rate because it compounds only once a year:
ER Bank Two = (1 + 0.07375)1 - 1 = 1.07375 - 1
After computing these values, we will subtract the effective rate of Bank Two from that of Bank One to determine the difference. By comparing the effective rates, we can conclude which bank offers the lower cost of borrowing and thus decide on the better option. Keep in mind, choosing the lower effective rate will typically result in less interest paid over the life of the loan.