Exam 7: Applications of Simple Interest

A $500,000 268-day Treasury Bill was issued to Buyer #1 at 4.1 % simple interest. 168 days before the T-Bill reached maturity it was sold by Buyer #1 at a rate that would provide Buyer #2 with a return of 3.4% if Buyer #2 held the T-Bill to maturity. What annual simple rate did Buyer #1 actually realize over the period that Buyer #1 held the T-Bill?

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% simple interest 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?

Calculate missing value for the promissory note:

On May 1, Gladis borrowed $10,000 on a line of credit with an annual rate of 7.75%. On August 15, Gladis repaid half of the loan. From August 15 to December 31, the interest rate decreased to an annual rate of 7.50%. Determine the total simple interest charged from May 1 to December 31, when Gladis repaid all obligations.

Calculate missing value for the promissory note:

A savings account pays interest of 1.5% simple interest. Interest is calculated on the daily closing balance and paid at the close of business on the last day of the month. A depositor had a $2,239 opening balance on September 1, deposited $734 on September 7 and $627 on September 21, and withdrew $300 on both September 10 and September 21. What interest will be credited to the account at the month's end?

For principal amounts of $5,000 to $49,999, a bank pays an interest rate of 0.95% on 180- to 269-day non-redeemable GICs, and 1.00% on 270- to 364-day non-redeemable GICs. Ranjit has $10,000 to invest for 364 days. Because he thinks interest rates will be higher six months from now, he is debating whether to choose a 182-day GIC now (and reinvest its maturity value in another 182-day GIC) or to choose a 364-day GIC today. What would the simple interest rate on 182-day GICs have to be on the reinvestment date for both alternatives to yield the same maturity value 364 days from now?

What do you need to know to be able to calculate the fair market value of an investment that will deliver two future payments?

A contract requires payments of $1,500, $2,000, and $1,000 in 100, 150, and 200 days, respectively, from today. What is the value of the contract today if the payments are discounted to yield a 3.5% simple interest rate of return?

Paul has $20,000 to invest for 6 months. For this amount, his bank pays 1.3% simple interest on a 90-day GIC and 1.5% on a 180-day GIC. If the interest rate on a 90-day GIC is the same 3 months from now, how much more interest will Paul earn by purchasing the 180-day GIC than by buying a 90-day GIC and then reinvesting its maturity value in a second 90-day GIC?

On January 12, Alex has student loans totalling $14,000. Alex agreed to a $200 per month repayment schedule at which time the annual interest rate was 5.5% simple interest. Determine the balance of the loan at the end of January.

Determine the legal due date for a three-month promissory note dated October 6, 2016.

Joan has savings of $12,000 on June 1. Since she may need some of the savings during the next 3 months, she is considering two options at her bank. (1) An Investment Builder savings account earns a 0.25% rate of interest. The interest is calculated on the daily closing balance and paid on the first day of the following month. (2) A 90- to 179-day cashable term deposit earns a rate of 0.8%, paid at maturity. If simple interest rates do not change and Joan does not withdraw any of the funds, how much more will she earn from the term deposit up to September 1? (Keep in mind that savings account interest paid on the first day of the month will itself subsequently earn interest during the subsequent month.)

The local bank pays simple interest calculated on the daily closing balance and paid monthly as follows: $0 to $5,000, 0.167%, $5,000 to $25,000, 0.25%, and over $25,000, 0.33%. Mrs. Singh had $3500 in her account on March 1. She deposited $2475 on March 5, withdrew $500 on March 12, and deposited $600 on March 15. Calculate the interest that she will be paid for the month of March.

On September 12, Claire had $8,000 in student loans outstanding. She agreed to $125 per month payments to repay these loans. From September 12 to October 8, the simple interest rates were 5.0%, but decreased to 4.5% thereafter. Calculate the balance outstanding on October 31.

Suppose that the current rates on 60 and 120-day GICs are 1.50% and 1.75% simple interest, respectively. An investor is weighing the alternatives of purchasing a 120-day GIC versus purchasing a 60-day GIC and then reinvesting its maturity value in a second 60-day GIC. What would the interest rate on 60-day GICs have to be 60 days from now for the investor to end up in the same financial position with either alternative?

Calculate the maturity value of a 120-day, $1,000 face value note dated September 5, 2016, earning interest at 4.75%.

A conditional sale contract requires two payments 3 and 6 months after the date of the contract. Each payment consists of $1,900 principal plus simple interest at 10.5% on $1,900 from the date of the contract. One month into the contract, what price would a finance company pay for the contract if it requires an 16% rate of return on its purchases?

Calculate missing value for the promissory note:

Suppose that the current rates on 90-and 180-day GICs are 3.25% and 3.50% simple interest, 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?