Which of the following? one-year $1,000 bank loans offers the lowest effective annual? rate?
a. A loan with an APR of 5.6%?, compounded monthly.
Since the APR is 5.6%?, the monthly rate is 0.567%, 0.367% or 0.467%. This translates to an effective annual rate of 5.8%, 5.9% or 5.7%.
b. A loan with an APR of 5.6%?, compounded? annually, that also has a compensating balance requirement of 10.2% ?(on which no interest is? paid).
The compensating balance is $112, $92,or $102. Therefore, the borrower will have use of only $908, $888, or $898 of the $1,000. The interest is $56, $58, or $54. The interest rate per period is 6.1%. 6.3%, or 6.2%. Since this alternative assumes annual? compounding, the effective annual rate is 6.1%. 6.3%, or 6.2% as well.
c. A loan with an APR of 5.6%?, compounded? annually, that has a 1.4% loan origination fee.
The interest expense is $56, $54, or $58, and the loan origination fee is $14, $14, or $15. The loan origination fee reduces the usable proceeds of the loan to $986, $985 or $987 because it is paid at the beginning of the loan. The interest rate per period is 7.0%. 7.2% or 7.1%. Since the loan is compounded annually in this? case, 7.0%. 7.2% or 7.1% is the effective annual rate.
Thus, alternative (a), (b) or (c) offers the lowest effective annual cost.