Question

Your company is considering a 1-year loan and has received the following proposals:

1.         Bank A offers a discount interest term loan with a stated 6.9% interest rate compounded annually and a compensating balance of 7.1%. Payments are made monthly.

2.         Bank B offers a term loan at a stated interest rate of 7.2% compounded weekly. Payments are made weekly.

3.         Bank C offers a term loan at a stated interest rate of 7.0% compounded monthly and with a compensating balance of 6%. Payments are made monthly.

4.         Bank D offers a discount interest term loan at a stated interest rate of 6.95% compounded every 6 months. Payments are made monthly.

Required:

Explain which loan proposal you would recommend your company accept based on the effective cost only.

Answer 1

Based on effective cost which means effective interest rate, so for that we calculate the effective iterest rate of each proposal one by one

1.         Bank A offers a discount interest term loan with a stated 6.9% interest rate compounded annually and a compensating balance of 7.1%. Payments are made monthly.

Effective interest rate = (Annualized interest paid on full amount borrowed – Annualized interest
received on cash deposited to meet compensating balance requirement, if any) / Amount of the Loan – Additional amount required to be kept on deposit to meet the compensating balance requirement

or

another way

first we found effective annual compund interest = 6.9% / 12 = 0.575% per month

Effective annual interest without copanssating balance =( 1 + 0.575% )12 - 1 = 1.0712 - 1 = 0.0712 = 7.12%

Effective annual interest rate with compansating balance = 7.12 / 100 - 7.1 =7.12 / 92.9 = 0.0766 = 7.66%

2.         Bank B offers a term loan at a stated interest rate of 7.2% compounded weekly. Payments are made weekly.

Effective annual interest rate = (1 + r / n )n − 1

Effective annual interest rate = (1 + 7.2% / 52)52 - 1

Effective annual interest rate = ( 1+ 0.138%)52 - 1

Effective annual interest rate = 1.0743 - 1 = 0.743 = 7.43%

3.         Bank C offers a term loan at a stated interest rate of 7.0% compounded monthly and with a compensating balance of 6%. Payments are made monthly.

Effective annual interest rate = (1 + r / n )n − 1

first we calculate effective annual interest rate compund monthly = ( 1 + 7% / 12)12 - 1

= ( 1 + 0.583% )12 - 1 = 1.0722 - 1 = 0.0722 = 7.22%

Effective annual interest rate with compansating balance = 7.22 / 100 - 6 = 7.22 / 94 = 0.0768  = 7.68%

4.         Bank D offers a discount interest term loan at a stated interest rate of 6.95% compounded every 6 months. Payments are made monthly.

Here we fist calculate effective interest rate compound half yearly = (1 + r / n )n − 1

= ( 1 + 6.95% / 2 )2 - 1 = ( 1+ 3.475% )2 - 1 = 1.0707 - 1 = 0.0707 = 7.07%

After calculate discount effect, which means they already take the interest from loan amt, so we get the money after take back the discounted amount

Effective annual interest rate = 7.07% / 100- 6.95 = 7.07 / 93.05 = 0.076 = 7.6%

Effective cost

Proposal A	7.66%
B	7.43%
C	7.68%
D	7.6%

Explain which loan proposal you would recommend your company accept based on the effective cost only.

Based on Effective cost of interest we take the proposal B for our company, because it has less effective cost of interest compire to another proposal