"16. If you borrow $12,000 at $900 interest for one year, what is your effective interest rate forthe following payment plans? a. Annual payment. b. Semiannual payments. c. Quarterly payments. d. Monthly payments.8-16. Solution:a. $900/$12,000 = 7.5%Use formula 8-6 for b, c, and d.Rate on installment loan =2×× Annual no. of payments Interest Total no. of payments + 1 × Principal ( ) b. (2 × 2 × $900)/(3 × $12,000) = $3,600/$36,000 = 10.00%c. (2 × 4 × $900)/(5 × $12,000) = $7,200/$60,000 = 12.00%d. (2 × 12 × $900)/(13 × $12,000) = $21,600/$156,000 = 13.85%S8-16 17. Vroom Motorcycle Company is borrowing $30,000 from First State Bank. The totalinterest is $9,000. The loan will be paid by making equal monthly payments for the nextthree years. What is the effective rate of interest on this installment loan?8-17. Solution:Vroom Motorcycle CompanyRate on installment loan =2×× Annual no. of payments Interest Total no. of payments + 1 × Principal ( ) 2×× 12 $9,000 $216,000 = = =19.46% 36+× 1 $30,000 $1,110,000 ( ) 18. Mr. Paul Promptly is a very cautious businessman. His supplier offers trade credit terms of3/10, net 70. Mr. Promptly never takes the discount offered, but he pays his suppliers in 60 days rather than the 70 days allowed so he is sure the payments are never late. What is Mr. Promptly’s cost of not taking the cash discount?8-18. Solution:Paul PromptlyDiscount % 360 Cost of not taking = × a cash discount 100%-- Disc.% Payment date Discount period 3% 360 = ×100%-- 3% 60 10 =3.09%×= 7.2 22.25% In this problem, Mr. Promptly has the use of funds for 50 extradays (60-10), instead of 60 extra days (70-10). Mr. Promptly’ssuppliers are offering terms of 3/10, net 70. Mr. Promptly iseffectively accepting terms of 3/10, net 60.S8-17 19. The Ogden Timber Company buys from its suppliers on terms of 2/10, net 35. Ogden hasnot been utilizing the discount offered and has been taking 50 days to pay its bills. Thesuppliers seem to accept this payment pattern, and Ogden’s credit rating has not been hurt.Mr. Wood, Ogden Timber Company’s vice-president, has suggested that the companybegin to take the discount offered. Mr. Wood proposes that the company borrow from itsbank at a stated rate of 15 percent. The bank requires a 25 percent compensating balance on these loans. Current account balances would not be available to meet any of thiscompensating balance requirement. Do you agree with Mr. Wood’s proposal?8-19. Solution:The Ogden Timber CompanyDiscount % 360 Cost of not taking a cash = × discount 100%- Disc.% Final due date- Discount period 2% 360 = × = 2.04%×= 9 18.36% 98% 50 -10 We use 50 days instead of 35 days as the final due date becauseOgden’s suppliers have effectively made this the due date eventhough the stated due date is 35 days.Effective rate of interest with a 25% compensating balancerequirement:= Interest rate/(1 – C)= 15%/(1 – .25)= 15%/(.75) = 20%The effective cost of the loan, 20%, is more than the cost ofpassing up the discount, 18.36%. Ogden Timber Company shouldcontinue to pay in 50 days and pass up the discount.S8-18 20. In problem 19, if the compensating balance requirement were 10 percent instead of 25 percent, would you change your answer? Do the appropriate calculation.8-20. Solution:The Ogden Time Company (Continued)Effective rate of interest with a 10% compensating balancerequirement:Interest rate 15% 15% = = = =16.67%1-- C 1 .1 .9 ( ) ( ) ( ) The answer now changes. The effective cost of the loan, 16.67%,is less than the cost of passing up the discount. Ogden TimberCompany should borrow the funds and take the discount.21. Bosworth Petroleum needs $500,000 to take a cash discount of 2/10, net 70. A banker willloan the money for 60 days at an interest cost of $8,100. a. What is the effective rate on the bank loan? b. How much would it cost (in percentage terms) if Bosworth did not take the cashdiscount, but paid the bill in 70 days instead of 10 days? c. Should Bosworth borrow the money to take the discount? d. If the banker requires a 20 percent compensating balance, how much must Bosworthborrow to end up with the $500,000? e. What would be the effective interest rate in part d if the interest charge for 60 dayswere $13,000? Should Bosworth borrow with the 20 percent compensating balance?(There are no funds to count against the compensating balance requirement.)S8-19 8-21. Solution:Bosworth Petroleum$8,100 360 a.Effective rate of interest = × $500,000 60 =1.62%×= 6 9.72% 2% 360 b. Cost of lost discount = × 98% 70 -10 ( ) = 2.04%×= 6 12.24% c. Yes, because the cost of borrowing is less than the cost oflosing the discount.Amount d. $500,000 $500,000 $500,000 = = = $625,000 needed to be1-- C 1 .20 .80 ( ) ( ) borrowed $13,000 360Effective interest rate = × e.$625,000 -125,000 60 $13,000 = ×= 6 2.6%×= 6 15.6% $500,000 No, do not borrow with a compensating balance of 20 percentsince the effective rate is greater than the savings from takingthe trade discount.S8-20 "