Chapter $8$Problems$1.$Cash discount $($LO$1)$ Compute the cost of not taking the following cash discounts.a$\mathrm{.}2/10,$ net $40.$b$\mathrm{.}2/15,$ net $30.$c$\mathrm{.}2/10,$ net $45.$d$\mathrm{.}3/10,$ net $90\mathrm{.}3.$Cash discount decision $($LO$1)$ Simmons Corp. can borrow from its bank at $17$ percent to take a cash discount. The terms of the cash discount are $1\mathrm{.}5/10,$ net $45.$ Should the firm borrow the funds?$4.$Effective rate of interest $($LO$2)$ Your bank will lend you $$4,000$ for $45$ days at a cost of $$50$ interest. What is your effective rate of interest?$6.$Effective rate on discounted loan $($LO$2)$ Sol Pine borrows $$5,000$ for one year at $13$ percent interest. What is the effective rate of interest if the loan is discounted?$8.$Prime vs$.$ LIBOR $($LO$2)$ Dr$.$ Ruth is going to borrow $$5,000$ to help write a book. The loan is for one year and the money can either be borrowed at the prime rate or the LIBOR rate. Assume the prime rate is $11$ percent and LIBOR $1\mathrm{.}5$ percent less. Also assume there will be a $$45$ transaction fee with LIBOR $($this amount must be added to the interest cost with LIBOR$).$ Which loan has the lower effective interest cost?$9.$Foreign borrowing $($LO$2)$ Gulliver Travel Agencies thinks interest rates in Europe are low. The firm borrows euros at $9$ percent for one year. During this time period the dollar falls $14$ percent against the euro. What is the effective interest rate on the loan for one year? $($Consider the $14$ percent fall in the value of the dollar as well as the interest payment.$)10.$Dollar cost of a loan $($LO$2)$ Talmud Book Company borrows $$24,900$ for $60$ days at $12$ percent interest. What is the dollar cost of the loan?$13.$Compensating balances $($LO$2)$ Digital Access Inc. needs $$400,000$ in funds for a project.a$.$With a compensating balance requirement of $20$ percent, how much will the firm need to borrow?b$.$Given your answer to part a and a stated interest rate of $9$ percent on the total amount borrowed, what is the effective rate on the $$400,000$ actually being used?$18.$Effective rate under different terms $($LO$2)$ If you borrow $$5,300$ at $$400$ interest for one year, what is your effective interest rate for the following payment plans?a$.$Annual payment.b$.$Semiannual payments.c$.$Quarterly payments.d$.$Monthly payments$\mathrm{.}21.$Cash discount under special circumstance $($LO$2)$ Mr$.$ Hugh Warner is a very cautious businessman. His supplier offers trade credit terms of $3/15,$ net $85.$ Mr$.$ Warner never takes the discount offered, but he pays his suppliers in $75$ days rather than the $85$ days allowed so he is sure the payments are never late. What is Mr$.$ Warners cost of not taking the cash discount?$24.$Bank loan to take cash discount $($LO$1$ and $2)$ Neveready Flashlights Inc. needs $$340,000$ to take a cash discount of $3/17,$ net $72.$ A banker will loan the money for $55$ days at an interest cost of $$10,400.$a$.$What is the effective rate on the bank loan?b$.$How much would it cost $($in percentage terms$)$ if the firm did not take the cash discount, but paid the bill in $72$ days instead of $17$ days?c$.$Should the firm borrow the money to take the discount?d$.$If the banker requires a $20$ percent compensating balance, how much must the firm borrow to end up with the $$340,000?$e$.$What would be the effective interest rate in part d if the interest charge for $55$ days were $$13,000?$ Should the firm borrow with the $20$ percent compensating balance? $($The firm has no funds to count against the compensating balance requirement.$)$