based on continuous compounding:

(a) What was the effective annual interest rate? (b) What was the nominal annual interest rate?

Minicases

3-56 The local garbage company charges $6 a month A for garbage collection. It had been their practice to send out bills to their 100,000 customers at the end of each 2-month period. Thus, at the end of February it would send a bill to each customer for $12 for garbage collection during January and

February. Recently the firm changed its billing date: it now

sends out the 2-month bills after one months service has been performed. Bills for January and February, for example, are sent out at the end of January. The local newspaper points out that the firm is receiv- ing half its money before the garbage collection. This unearned money, the newspaper says, could be temporarily invested for one month at 1% per month interest by the garbage company to earn extra income.

Compute how much extra income the garbage company could earn each year if it invests the money as described by the newspaper.

3-57 The Apex Company sold a water softener to Marty Smith. The price of the unit was $350. Marty asked for a deferred payment plan, and a contract was writ- ten. Under the contract, the buyer could delay paying for the water softener if he purchased the coarse salt for recharging the softener from Apex. At the end of 2 years, the buyer was to pay for the unit in a lump sum, with interest at a quarterly rate of 1.5%. According to the contract, if the customer ceased buying salt from Apex at any time prior to 2 years, the full payment due at the end of 2 years would automatically become due.

Six months later, Marty decided to buy salt elsewhere and stopped buying from Apex, where- upon Apex asked for the full payment that was to have been due 18 months hence. Marty was unhappy about this, so Apex offered as an alternative to accept the $350 with interest at 10% per semiannual period for the 6 months. Which alternative should Marty accept? Explain.

3-58 The U.S. recently purchased $1 billion of 30-year zero-coupon bonds from a struggling foreign nation. The bonds yield 41/2% per year interest. Zero coupon

A

month, compounded continuously, on its customers charge accounts. What is the nominal annual interest rate? What is the effective interest rate?