Exam 6: Measuring and Calculating Interest Rates and Financial Asset Prices

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Using the yield-approximation formula discussed in your text, determine the average annual yield on a bond whose current price is $1,100, par value is $1,000, coupon rate is 12 percent and whose term to maturity is ten years. Your answer is (to the nearest tenth of a percent):

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A

See if you can explain the meaning of the following terms and, where a formula is involved, explain the components of each formula:

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a. Simple interest - A method of determining the interest rate on a loan in which interest is assessed only for the period of time the borrower actually has use of loanable funds.
b. Add-on interest - Interest on a loan is calculated on the full principal amount owed. The interest owed is then added to the principal and divided by the number of payments to determine the size of each installment payment that must be made.
c. Discount method - Borrower pays interest on a loan up front and receives total loan amount less interest due.
d. APR - Actual rate on a loan, reflecting all credit costs and adjusted for the declining amount owed on an installment loan, that must be quoted household borrowers under federal law.
e. Compounding of interest - A lender or depositor of funds earns interest income on both the principal amount of any funds owed and on accumulated interest as well.
f. APY - Annual percentage yield on a deposit, which adjusts for the average balance in the account and any fees charged the depositor and must be reported to the depositor before opening a new account.

A commercial loan extended to CIBER-LAND Corporation for $2.5 million assesses an interest charge of $350,000 up front. Using the discount method of calculating loan rates, what is the effective interest rate on this loan? Suppose that instead of deducting the interest owed up front the company's lender agrees to extend the full $2.5 million and add the amount of interest owed to the face of CIBER's note. What then is the loan's effective interest rate?

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Using the discount interest formula: $350,000/($2,500,000-$350,000) = 16.28%. For the second part, multiply $2,500,000 times (1+ 0.1628) = $2,907,000. Here again, $407,000/($2,907,000-$407,000) = 16.28%.

You have just placed $1,500 in a bank savings deposit and plan to hold that deposit for eight years, earning 5-1/2 percent per annum. If the bank compounds interest daily, what will be the total value of the deposit in eight years? How does your answer change if the bank switches to monthly compounding? Quarterly compounding?

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An AAA-rated corporate bond has a current market price of $800 and will pay $100 in interest for ten years. If its par value is $1,000, what is its yield to maturity?

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A home mortgage loan for $60,000 is available from the neighboring bank at an interest rate of one percent per month. The loan will mature in 25 years. What payment must the borrower make each month under the terms of this loan agreement?

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An investor is interested in purchasing a new 20-year government bond carrying a 10 percent coupon rate. The bond's current market price is $875 for a $1,000 par value instrument. If the investor buys the bond at the going price and holds to maturity, what will be his yield to maturity?

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Suppose a 10-year bond is issued with a coupon rate of 8 percent when the market rate of interest is also 8 percent and the future market rate rises to 9 percent, what happens to the price of this bond? What happens to the bond's price if the market rate falls to 6 percent? Explain why?

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You decide to take out a 30-year mortgage loan to buy the home of your dreams. The home's purchase price is $120,000. You manage to scrape together a $20,000 down payment and plan to borrow the balance of the purchase price. Hardy Savings and Loan Association quotes you a fixed annual loan rate of 12 percent. What will your monthly payment be?

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What is different about interest rates or the price of credit, from other prices in the economy?

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What exactly is a basis point? Why is it an important interest-rate measure?

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You discover a $1,000 par value bond just issued by XYC Corporation that pays interest semiannually at a coupon rate of 12 percent. The bond will mature in 10 years and can be purchased today at a price of $900 including the broker's commission. What is the bond's yield to maturity if all payments are made on time?

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In problem 7 above, if interest were compounded monthly, instead of annually, what lump sum amount would be due in five years and how much total interest must be paid?

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A depositor leaves her funds in the amount of $5,000 in a credit union deposit for a full year but then withdraws $1000 after 270 days. At the end of the year the credit union pays her $300 in interest. What is this depositor's daily average balance and APY?

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You borrow $2,500 for five years at a rate of 12 percent per annum, compounded annually. What is the lump sum amount due at the end of the 5 years? What is the total amount of interest owed?

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What assumptions underlie the calculation of the yield to maturity?

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How is the monthly payment that a home mortgage borrower must meet determined? Why is it that payments made early in the life of a typical home mortgage go largely to pay interest rather than repay principal?

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You plan to borrow $2,000 in order to take a vacation and want to repay the loan in a year. The banker offers you a simple interest rate of 12% with repayments in equal installments six months and twelve months from now. What is your total interest bill?

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