Both Bond Sam and Bond Dave have 9 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, wheareas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, the percentage change in the price of Bonds Sam and Dave is ? percent and ? percent, respectively. (Do not include the percent signs (%). Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16)) If rates were to suddenly fall by 2 percent instead, the percentage change in the price of Bonds Sam and Dave is ? percent and ?percent, respectively.

-3% -14%

To find the percentage change in the price of the bonds, we need to use the bond price formula:

Price = (Coupon Payment / (1 + YTM/2)) + (Coupon Payment / (1 + YTM/2)²) + ... + (Coupon Payment / (1 + YTM/2)^2n) + (Face Value / (1 + YTM/2)^2n)

Where:
- Coupon Payment is the semiannual coupon payment
- YTM is the Yield to Maturity
- n is the number of semiannual periods remaining until maturity
- Face Value is the par value of the bond

Let's start with Bond Sam:
- Coupon Payment = 9% * Face Value / 2
- YTM = 2% (as interest rates rise by 2%)
- n = 3 years * 2 semiannual periods per year = 6
- Face Value is given as par value, so it remains constant at 100.

We substitute these values into the bond price formula and calculate the new price:

New Price (Rising rates) = (4.5 / (1 + 0.02/2)) + (4.5 / (1 + 0.02/2)²) + ... + (4.5 / (1 + 0.02/2)^12) + (100 / (1 + 0.02/2)^12)

Now we can calculate the percentage change in the price of Bond Sam when rates rise:

Percentage Change (Rising rates) = (New Price - Price) / Price * 100

Next, let's calculate for Bond Dave:
- Coupon Payment = 9% * Face Value / 2
- YTM = 2% (as interest rates rise by 2%)
- n = 20 years * 2 semiannual periods per year = 40

We substitute these values into the bond price formula and calculate the new price:

New Price (Rising rates) = (4.5 / (1 + 0.02/2)) + (4.5 / (1 + 0.02/2)²) + ... + (4.5 / (1 + 0.02/2)^40) + (100 / (1 + 0.02/2)^40)

Now we can calculate the percentage change in the price of Bond Dave when rates rise:

Percentage Change (Rising rates) = (New Price - Price) / Price * 100

Finally, to find the percentage change when rates fall by 2%, you need to follow the same steps but substitute YTM with -2%:

Percentage Change (Falling rates) = (New Price - Price) / Price * 100

Perform these calculations and round the answers to 2 decimal places.