Exam 7: Applications of Simple Interest

Suppose that the current rates on 90-and 180-day GICs are 3.25% and 3.50%, respectively. An investor is weighing the alternatives of purchasing a 180-day GIC versus purchasing a 90-day GIC and then reinvesting its maturity value in a second 90-day GIC. What would the interest rate on 90-day GICs have to be 90 days from now for the investor to end up in the same financial position with either alternative?

Over the past 35 years, the prevailing market yield or discount rate on 90-day T-bills has ranged from a low of 0.17% in February 2010 to a high of 20.82% in August of 1981. (The period from 1979 to 1990 was a time of historically high inflation rates and interest rates.) How much more would you have paid for a $100,000 face value 90-day T-bill at the February 2010 discount rate than at the August 1981 discount rate?

An investment promises two payments of $500, 90 and 150 days from today. What price will an investor pay today if her required rate of return is 6.5%?

An assignable loan contract executed three months ago requires two payments to be paid five and ten months after the contract date. Each payment consists of a principal portion of $1,800 plus interest at 5% on $1,800 from the date of the contract. The payee is offering to sell the contract to a finance company in order to raise cash. If the finance company requires a return of 10%, what price will it be prepared to pay today for the contract?

For investments of $5,000 to $24,999, a bank quotes interest rates of 2.65% on 90-day GICs and 2.85% on 180-day GICs. How much more interest will an investor earn by placing $15,000 in a 180-day GIC than by purchasing two consecutive 90-day GICs? (Assume that interest rates do not change over the next 90 days. Remember that interest earned from the first 90-day GIC can be invested in the second 90-day GIC.)

George borrowed $4,000 on demand from CIBC on January 28 for an RRSP contribution. Because he used the loan proceeds to purchase CIBC's mutual funds for his RRSP, the interest rate on the loan was set at the bank's prime rate. George agreed to make monthly payments of $600 (except for a smaller final payment) on the twenty-first of each month, beginning February 21. The prime rate was initially 3.75%, dropped to 3.5% effective May 15, and decreased another 0.25% on July 5. It was not a leap year. Construct a repayment schedule showing the amount of each payment and the allocation of each payment to interest and principal.

A $100,000, 90-day commercial paper certificate issued by Bell Canada Enterprises was sold on its issue date for $98,950. What annual rate of return (to the nearest 0.001%) will it yield to the buyer?

Shoreline Yachts has a $1 million line of credit with the Royal Bank secured by its inventory of sailboats. Interest is charged at the floating (naturally!) rate of prime plus 2% on the 10^th of each month (for days up to but not including the 10^th). On February 10 (of a non-leap year), the loan balance stood at $770,000 and the prime rate at 6.5%. Shoreline took an additional $100,000 draw on March 1. Spring sales enabled Shoreline to make payments of $125,000 and $150,000 against the principal on March 30 and April 28. The prime rate rose by 0.5% on April 8. What total interest was Shoreline charged for the 3 months from February 10 to May 10? Present a repayment schedule showing how this interest figure was determined.