please help with the following question.

8. Which of the following one-year $1,000 bank loans offers the lowest effective annual rate?

a. A loan with an APR of 6.1%, compounded monthly.

b. A loan with an APR of 6.1%, compounded annually, that also has a compensating balance requirement of 9.7% (on which no interest is paid).

c. A loan with an APR of 6.1%, compounded annually, that has a 1.4% loan origination fee.

a. A loan with an APR of 6.1%, compounded monthly.(Select from the drop-down menus.)

Since the APR is 6.1%, the monthly rate is: A. 0.508%, B. 0.708%, or C. 0.308%

This translates to an effective annual rate of A. 6.1%, B. 6.5%, or C. 6.3%

b. A loan with an APR of 6.1%, compounded annually, that also has a compensating balance requirement of 9.7% (on which no interest is paid).(Select from the drop-down menus.)

The compensating balance is A. $117, B. $77, or C. $97

Therefore, the borrower will have use of only A. $923, B. $903, C. $883 of the $1,000.

The interest is A. $65, b. $57,or C. $61

The interest rate per period is A. 6.8%, B. 7.0%, or C. 6.6%

Since this alternative assumes annual compounding, the effective annual rate is A. 6.6%, B. 7.0%, or C. 6.8%

c. A loan with an APR of 6.1%, compounded annually, that has a 1.4% loan origination fee.

The interest expense is A. $57, B. $65, or C. $61and the loan origination fee is A. $12, B. $16, or C. $14

The loan origination fee reduces the usable proceeds of the loan to A.. $984, B. $988, or C. $986

because it is paid at the beginning of the loan. The interest rate per period is A. 7.4%, B. 7.8%, or C. 7.6%

Since the loan is compounded annually in this case, A. 7.8%, B. 7.4% or C. 7.6%is the effective annual rate.

Thus, alternative (A), (B) (C) offers the lowest effective annual cost.

8. Which of the following one-year $1,000 bank loans offers the lowest effective annual rate?

a. A loan with an APR of 6.1%, compounded monthly.

b. A loan with an APR of 6.1%, compounded annually, that also has a compensating balance requirement of 9.7% (on which no interest is paid).

c. A loan with an APR of 6.1%, compounded annually, that has a 1.4% loan origination fee.