16.The duration of an 11-year, $1,000 Treasury bond paying a 10 percent semiannual coupon and selling at par has been estimated at 6.763 years.

a.What is the modified duration of the bond? What is the dollar duration of the bond?

Modified duration = D/(1 + R/2) = 6.763/(1 + .10/2) = 6.441 years

Dollar duration = MD x P = 6.441 x $1,000 = 6441

b.What will be the estimated price change on the bond if interest rates increase0.10 percent (10 basis points)?If rates decrease 0.20 percent (20 basis points)?

For interest rates increase of0.10 percent:

Estimated change in price = - dollar duration x DR = -6441 x 0.001 = -$6.441

=> new price = $1,000 - $6.441 = $993.559

For interest rates decrease of0.20 percent:

Estimated change in price = -6441 x -0.002 = $12.882

=> new price = $1,000 + $12.882 = $1,012.882

c.What would the actual price of the bond be under each rate change situation in part (b) using the traditional present value bond pricing techniques? What is the amount of error in each case?

RatePriceActual

ChangeEstimatedPriceError

+ 0.001$993.559$993.535$0.024

- 0.002$1,012.882$1,013.111-$0.229

I DONT UNDERSTAND HOW THEY CALCULATED THE ACTUAL PRICES. 993.535 AND 1013.111 please show how to calculate