A 20-year bond priced to have an annual effective yield of 10% has a Macaulay duration of 11. Immediately after the bond is priced, the market yield rate increases by 0.25%. The bond's approximate percentage price change, using a first-order Macaulay approximation, is X.

Calculate X.

• –2.22%
• –2.47%
• –2.50%
• –2.62%
• –2.75%

Krishna buys an n-year 1000 bond at par. The Macaulay duration is 7.959 years using an annual effective interest rate of 7.2%.

Calculate the estimated price of the bond, using the first-order Macaulay approximation, if the interest rate rises to 8.0%.

• 940.60
• 942.54
• 944.56
• 947.03
• 948.47

A bond has a modified duration of 8 and a price of 112,955 calculated using an annual effective interest rate of 6.4%. [math]E_{MAC}[/math] is the estimated price of this bond at an interest rate of 7.0% using the first-order Macaulay approximation. [math]E_{MOD}[/math] is the estimated price of this bond at an interest rate of 7.0% using the first-order modified approximation.

Calculate [math]E_{MAC}-E_{MOD}[/math].

• 91
• 102
• 116
• 127
• 143

SOA Life Insurance Life Insurance Company has a portfolio of two bonds:

• Bond 1 is a bond with a Macaulay duration of 7.28 and a price of 35,000; and
• Bond 2 is a bond with a Macaulay duration of 12.74 and a price of 65,000

The price and Macaulay duration for both bonds were calculated using an annual effective interest rate of 4.32%. Bailey estimates the value of this portfolio at an interest rate of i using the first-order Macaulay approximation to be 105,000.

Determine i.

• 3.49%
• 3.62%
• 3.85%
• 3.92%
• 4.03%

Graham is the beneficiary of an annuity due. At an annual effective interest rate of 5%, the present value of payments is 123,000 and the modified duration is [math]D_{MOD}[/math].

Tyler uses the first-order Macaulay approximation to estimate the present value of Graham’s annuity due at an annual effective interest rate was 5.4%. Tyler estimates the present value to be 121,212.

Calculate [math]D_{MOD}[/math], the modified duration of Graham’s annuity at 5%.

• 3.67
• 3.75
• 3.85
• 3.95
• 4.04

An annuity provides the following payments:

1. X at the beginning of each year for 20 years, starting today
2. 4X at the beginning of each year for 30 years, starting 20 years from today

Calculate the Macaulay duration of this annuity using an annual effective interest rate of 2%

• 27.32
• 27.87
• 28.30
• 33.53
• 35.41

A company is considering a project that will require an initial investment of 600 and additional investments of 100 and 50 at the end of years one and two, respectively. It is expected that revenue from this project will be 150 per year for five years, beginning one year from the initial investment.

Assuming an annual effective rate of 15%, calculate the net present value of this project.

• –222
• –134
• 0
• 134
• 222

Consider a 7-year loan to be repaid with equal payments made at the end of each year. The annual effective interest rate is 10%.

Calculate the Macaulay duration of the loan payments.

• 3.15
• 3.29
• 3.40
• 3.50
• 3.62

A trucking company with assets and liabilities needs to choose between various ten-year par value bonds each with 8% annual effective yield rate and annual coupons. The bonds have varying face values and varying coupon rates. The company wants to analyze the effects of face value and coupon rate changes on Macaulay duration of these bonds, in order to choose an investment strategy that immunizes its position. Determine which of the following statements is true about the separate effects of face value and coupon rate changes on the duration of these bonds.

• Macaulay duration increases as face value increases, and increases as coupon rate increases.
• Macaulay duration increases as face value increases, and decreases as coupon rate increases.
• Macaulay duration remains constant as face value increases, and increases as coupon rate increases.
• Macaulay duration remains constant as face value increases, and remains constant as coupon rate increases.
• Macaulay duration remains constant as face value increases, and decreases as coupon rate increases

You are given the following information about a 30-year bond:

1. The par value is 2000.
2. The redemption value is 2250.
3. Coupons are paid annually.
4. The annual coupon rate is twice the annual yield rate.
5. The purchase price is 3609.29.
6. Based on the yield rate, the Macaulay duration of the bond is 14.41 years

Calculate the modified duration of the bond, based on the yield rate.

• 12.40 years
• 13.07 years
• 13.71 years
• 14.41 years
• 15.15 years