Part 2 Bond Valuation and Interest Rates

Exercise 1:APR and EAR Practice 1

APR and EAR Practice 1APR=period rate*m

APR (Q) - The Annual Percentage Rate (APR) is the annual rate required to reported by law.This is the same as the rate that we have been using all semester (r).It is equal to the period rate (rate per period) multiplied by the number of period per year (m).The APR does not capture the effect of compounding.

EARThe Effective Annual Rate EAR (EAR) is an annual interest rate that reflects the effect of compounding.An EAR will always be higher than an APR if the number of compounding periods per year is greater than 1.

period rate - this is the rate per period.For example, monthly rate, daily rate, weekly rate.

We have already been working with the period rate.Recall that if we were looking at an annuity with monthly payments and an annual rate of 6%.To use the annuity formula, we would divide the annual rate of 6% by 12 to get a monthly rate of .5%.This is the period rate.

"m" - number of compounding periods per year.Remember that when calculating EAR or APR, we are calculating ANNUAL rates.Therefore, m is always the number of periods PER YEAR.

Practice:

1.If a credit card charges a rate of 24.99% per year with daily compounding, what rate are you actually paying?

2.If an investment pays 14% per year with monthly compounding, what rate are you actually earning?

3.Your aunt gave you $300 to purchase a text book.You are going to pay her back $325 in 5 months.What is m? What is the period rate? What is the APR? What is the EAR?

4.You paid your $100 phone bill 10 days late and were charged a $15 late fee.What is the APR? What is the EAR?

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Exercise 2:APR and EAR Practice 2

1.Suppose that you want to borrow $1000 from your parents for a deposit on a new apartment.You promised your parents that you would pay them back six months from today.On top of the $1000 repayment, you will pay them an additional $100 for interest six months from now.

a.What is the period rate?

b.What is the APR (Q)?

c.What is the EAR?

Bond Valuation - Related Formulas

PV = FV / (1 + r)^t

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Exercise 3: Bonds Practice 3

1.- A bond has a coupon rate of 7% and pays coupons semi-annually.The bond matures in 15 years and the yield to maturity on similar bonds is 7.5%.Is this a par, premium or discount bond?What is the fair value of the bond?

2.A or B or A=B.Bond A has a coupon rate of 4% and sells at $1010.Bond B has a coupon rate of 4% and sells at $990.Which bond has a higher yield to maturity?

3.A bond is priced at $1001.50.Yield to maturity on similar bonds is 5%.What is the approximate coupon rate of the bond?Is it slightly lower or higher than 5%?

4.A bond is priced at $1025 and matures in 3 years.The bond pays coupons semi-annually.If the fair market yield on the bond is 4.5%, what is the bond's coupon payment? What is the bond's coupon rate?

5.True or False.If an investor has a very high tax rate she should probably choose a corporate bond over a municipal bond.

6.A or B or A=B.Bond A pays a $110 per year.Bond B has a coupon rate of 11%.Which bond has the higher price?

7. Find the price of the bond described in the table below.Assume the date is October 15, 2017