Mathematics, 02.11.2019 06:31 brmoen1392

Both bond sam and bond dave have 6 percent coupons, make semiannual payments, and are priced at par value. bond sam has five years to maturity, whereas bond dave has 18 years to maturity. if interest rates suddenly rise by 2 percent, what is the percentage change in the price of bond sam and bond dave?

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Answer from: harleycochran2ovyt3n

Bond Sam = -8.11%

Bond Dave = -18.9%

Step-by-step explanation:

Let the face value of bonds be $1,000.

Bond Sam :

Coupon rate = 6%

yield = 6%

The number of years to maturity = 5 years

market interest rate suddenly rise by 2% = 8%

To calculate the present value of the bond, find the semiannual coupon payment.

Semi-annual coupon payment = Face value × Annual coupon rate × $[\frac{6}{12}]$

= 1,000 × 6% × $[\frac{6}{12}]$

= $30

Now convert the annual market interest rate to semi-annual interest rate.

Semi-annual interest rate = $[\frac{\text{annual market rate of interest}}{2}]$

= $[\frac{0.08}{2}]$

= 4%

Number of years converted in semi-annual periods

5 years = 5 × 2 = 10 semiannual periods

Now use excel and select "fx" and choose "PV" and enter the values into the formula :

PV = (rate,nperiod,pmt,fv)

= (4%,10,-30,-1000)

= $918.89

Change in price of bond Sam = $\frac{918.89-1000}{1000}$

= -0.08111 or -8.11%

Bond Dave :

Coupon rate = 6%

yield = 6%

The number of years to maturity = 18 years

market interest rate suddenly rise by 2% = 8%

To calculate the present value of the bond, find the semiannual coupon payment.

Semi-annual coupon payment = Face value × Annual coupon rate × $[\frac{6}{12}]$

= 1,000 × 6% × $[\frac{6}{12}]$

= $30

Now convert the annual market interest rate to semi-annual interest rate.

Semi-annual interest rate = $[\frac{\text{annual market rate of interest}}{2}]$

= $[\frac{0.08}{2}]$

= 4%

Number of years converted in semi-annual periods

18 years = 18 × 2 = 36 semiannual periods

Now use excel and select "fx" and choose "PV" and enter the values into the formula :

PV = (rate,nperiod,pmt,fv)

= (4%,36,-30,-1000)

= $810.92

Change in price of bond Sam = $\frac{810.92-1000}{1000}$

= -0.18908 or -18.9%

Percentage change in the price of Bond Sam -8.11% and Bond Dave -18.9%.

Answer from: Quest

The answer is budget i believe. hope this but it’s self explanatory.

Answer from: Quest

b.an increase in a causes b to decrease

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