# Investment, Annual Return and Effective Rate

Assume all bonds have a face value of $1,000.00, unless otherwise informed

1. You buy an investment today for $9,825. You sell the investment in 90 days for $10,000.

a. What is the nominal annual return on this investment?

b. What is the effective annual rate on this investment?

2. A 10 year semi-annual payment corporate coupon bond has a coupon rate of 11% and a required return of 10%. The bond's market price is

3. Suppose we look in the newspaper and find the following rates: the rate on 1-year securities is 4.65%, on a similar 2-year security 6.30%, and a 3-year security 6.67%. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now?

4. Consider the following bonds:

a. What is the duration of a five-year bond with a 6.5 percent semiannual coupon if the yield to maturity (ytm) is 7.00%?

b. What is the duration of a 20-year zero coupon bond with a yield to maturity of 7.65%

c. You expect a sudden, but widely unanticipated, decrease in the market rates of interest due to a change in position by the Federal Reserve. Would you rather be holding in your asset portfolio the bond from a. above (BOND A) or the zero from b. above (BOND B)? Which bond would you prefer, and why?

5. If a $10,000 par T-Bill has a 4.5% discount quote and a 180 day maturity, what is the price of the T-Bill?

6. Ninety day commercial paper can be bought at a 4% discount. What are the bond equivalent yield and the effective annual rate on the commercial paper?

a. Why do these rates differ?

7. You purchase a $200,000 house and you pay 20% down. You obtain a fixed rate mortgage where the annual interest rate is 7% and there are 360 monthly payments. What is the monthly payment?

8. A Swiss bank converted 1 million Swiss francs to euros to make a euro loan to a customer when the exchange rate was 1.75 francs per euro. The borrower agreed to repay the principle plus 4% interest in 1 year. The borrower repaid euros at loan maturity and when the loan was repaid the exchange rate was 1.85 francs per EURO. What was the bank's franc rate of return?

9. At the beginning of the year the exchange rate between the Brazilian Real and the U.S. dollar is 2.5 Reals per dollar. Over the year Brazilian inflation is 16% and U.S. inflation is 2%. If purchasing power parity holds, at year end the exchange rate should be _____ dollars per real.

10. Why do mortgage lenders prefer ARMs while many borrowers prefer fixed rate mortgages, ceteris paribus?

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#### Solution Preview

Please try and complete practice problems leading to next week's exam. Assume all bonds have a face value of $1,000.00, unless otherwise informed

1. You buy an investment today for $9,825. You sell the investment in 90 days for $10,000.

a. [2] What is the nominal annual return on this investment?

Investment= $9,825

Selling value= $10,000

Number of days= 90 days

Number of days in a year= 365 days

Return over a period of 90 days= 1.78% =(10000 / 9825) -1

Nominal annual rate of return= 7.22% =1.78% x ( 365 / 90)

b. [3] What is the effective annual rate on this investment?

Effective annual rate on this investment= 7.42% ={(1+ 1.78%) ^ ( 365 / 90)} - 1

2. [4] A 10 year semi-annual payment corporate coupon bond has a coupon rate of 11% and a required return of 10%. The bond's market price is

To calculate the price of the bond we need to calculate / read from tables the values of

PVIF= Present Value Interest Factor

PVIFA= Present Value Interest Factor for an Annuity

Price of bond= PVIF * Redemption value + PVIFA * interest payment per period

PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%

PVIF( n, r%)= =1/(1+r%)^n

Price of bond

Coupon rate= 11.000%

Face value= $1,000

Interest payment per year= $110.00 =11.% x 1000

Frequency= S Semi Annual

No of years to maturity= 15

No of Periods=n= 30 =2x15

Discount rate annually= 10.00% (YTM)

Discount rate per period=r= 5.00% =10.%/2 Semi Annual

Price of bond=PVIFA X Interest Payment per period +PVIF X Redemption value

Interest payment per period= $55.00 =110/2

Redemption value= $1,000 =Face Value

PVIF (30 periods, 5.% rate)= 0.231377

PVIFA (30 periods, 5.% rate)= 15.372451

PVIFA X Interest Payment= $845.48 =15.372451*55

PVIF X Redemption value= $231.38 =0.231377*1000

Total= $1,076.86 =Price of bond

Answer: Price of bond= $1,076.86

3. [5] Suppose we look in the newspaper and find the following rates: the rate on 1-year securities is 4.65%, on a similar 2-year security 6.30%, and a 3-year security 6.67%. If the unbiased ...

#### Solution Summary

Answers Investment questions on nominal annual return, effective annual rate, bond's market price, one-year interest rate expected one year from now, duration of a five-year bond, decrease in the market rates of interest, discount quote, commercial paper, T-Bill, annuity, mortgage, foreign exchange rate, ARM, fixed rate mortgages

What is the annual effective rate earned on the investments portfolio? 2. What rate of return would have been calculated if one only looked at the ending portfolio value as compared with the beginning investment?

A Firm invests $1,000,000 at the beginning of the year. It adds another $250,000 at the end of the first quarter, withdraws $350,000 at the end of the second quarter, adds $145,000 at the end of the third quarter, and withdraws $450,000 of the remaining funds at the end of the year. It earns $20,000 of interest in the first quarter, $17,000 in the second quarter, $12,000 in the third quarter, and $29,000 in the fourth quarter.

1. What is the annual effective rate earned on the investments portfolio? (show work)

2. What rate of return would have been calculated if one only looked at the ending portfolio value as compared with the beginning $1,000,000 investment?

(show work)