Which one-year $1000 bank loan offers the lowest effective annual rate?

The loan with the lowest effective annual rate is option c, the loan with an APR of 6%, compounded annually, and a 1% loan origination fee.

To determine the lowest effective annual rate among the given options, we need to calculate the effective annual rate (EAR) for each loan.

a. Loan with an APR of 6%, compounded monthly:

The monthly interest rate can be calculated by dividing the APR by 12: 6% / 12 = 0.5%.

Since the loan is compounded monthly, the EAR can be calculated using the following formula:

EAR = (1 + Monthly Rate)^12 - 1

= (1 + 0.5%)^12 - 1

≈ 6.17%

b. Loan with an APR of 6%, compounded annually, with a 10% compensating balance:

In this case, the effective loan amount is reduced by the compensating balance. So, only 90% of the loan amount is effectively received.

The EAR can be calculated using the following formula:

EAR = (1 + APR / (1 - Compensating Balance))^n - 1

= (1 + 6% / (1 - 10%))^1 - 1

= (1 + 6% / 0.9) - 1

≈ 6.67%

c. Loan with an APR of 6%, compounded annually, with a 1% loan origination fee:

The loan origination fee is a one-time charge that reduces the effective loan amount by 1%.

The EAR can be calculated using the following formula:

EAR = (1 + APR)^n * (1 - Origination Fee) - 1

= (1 + 6%)^1 * (1 - 1%) - 1

= (1 + 6%)*(1 - 0.01) - 1

≈ 5.94%

Comparing the effective annual rates (EAR) calculated for each option:

a. 6.17%

b. 6.67%

c. 5.94%

To know more effective annual rate (EAR)