Assume that you can borrow $175,000 for one year from a local commercial bank. a. The bank loan officer offers you the loan if you agree to pay $16000 in interest plus repay the $175,000 at the end of one year. What is the percent interest rate or effective cost? b. As an alternative you can get a one year, $175,000 discount loan at 9 percent interest. What is the percent interest rate or effective cost? c. Which one of the two loans would you prefer? d. At what discount loan interest rate would you be indifferent between the two loans?
1.a. The effective rate is 9.1428571%
effective rate = 16000 divided by 175000 x 100= 0.091428571x 100
1.b. The effective rate is 9.89%
Interest is 15,750 computed as : 175000 x 9%
The net proceed of loan is $ 159,250 computed as : 175000 minus 15750
Effective rate is: computed as follows: 15,750/159250 x100= 9.89%
1.c Based on less cost, I would prefer Loan with 16000 interest payable at the end of the year.
2.At 8.375% discount rate, I would be indifferent to both loan.
Interest = 175000 x 8.375= 14656.25
Net proceed = 175000- 14656.25 =160343.75
Effective rate = 14656.25/160,343.75 x 100 = 9.14%
Note: Computation of 8.375% is based on trial and error method, where a high and low figures are used and interpolated figure is tried , with objective that effective rate will be equal to the other loan's effective rate.