Both Bond Sam and Bond Dave have 10 percent coupon bonds outstanding, with semiannual interest payments, and both are currently priced at the par value of $1,000. Bond Sam has three years to maturity, whereas the Bond Dave has 18 years to maturity.If interest rates suddenly rise by 2 percent, what is the percentage change in the price of each bond?

To calculate the percentage change in the price of each bond, we need to determine the new price of the bonds after the interest rates have risen by 2 percent.

First, let's calculate the new price of Bond Sam. Since Bond Sam has three years to maturity and semiannual interest payments, we need to calculate the present value of the bond's future cash flows using the new interest rate.

The new interest rate is the original interest rate plus the increase of 2 percent. So, the new interest rate for Bond Sam is 10 percent + 2 percent = 12 percent.

Using the new interest rate of 12 percent, we can calculate the present value of the bond's future cash flows. The coupon payment for Bond Sam is 10 percent of $1,000, which is$100. Since there are six semiannual periods in three years, the total number of periods is 6 * 3 = 18.

Using the present value formula for an annuity, we can calculate the present value of the bond's coupon payments:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the coupon payment, r is the interest rate per period, and n is the total number of periods.

PV = $100 * (1 - (1 + 0.12)^(-18)) / 0.12 PV =$100 * (1 - 0.198) / 0.12 PV = $100 * 0.802 / 0.12 PV =$802 / 0.12 PV = $6,683.33

Therefore, the new price of Bond Sam is $6,683.33.

Next, let's calculate the new price of Bond Dave. Since Bond Dave has 18 years to maturity and semiannual interest payments, we need to calculate the present value of the bond's future cash flows using the new interest rate.

Using the same process as before, the new interest rate for Bond Dave is 10 percent + 2 percent = 12 percent.

Using the present value formula for an annuity, we can calculate the present value of the bond's coupon payments:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the coupon payment, r is the interest rate per period, and n is the total number of periods.

PV = $100 * (1 - (1 + 0.12)^(-36)) / 0.12 PV =$100 * (1 - 0.376) / 0.12 PV = $100 * 0.624 / 0.12 PV =$624 / 0.12 PV = $5,200

Therefore, the new price of Bond Dave is $5,200.

To calculate the percentage change in the price of each bond, we can use the following formula:

Percentage Change = (New Price - Old Price) / Old Price * 100

For Bond Sam: Percentage Change = ($6,683.33 -$1,000) / $1,000 * 100 Percentage Change =$5,683.33 / $1,000 * 100 Percentage Change = 568.33%

For Bond Dave: Percentage Change = ($5,200 -$1,000) / $1,000 * 100 Percentage Change =$4,200 / $1,000 * 100 Percentage Change = 420%

Therefore, the percentage change in the price of Bond Sam is 568.33% and the percentage change in the price of Bond Dave is 420%.