An investor has two bonds in his portfolio that have a face value of $$1,000$ and pay an $11\%$ annual coupon. Bond $L$ matures in $11$ years, while Bond $S$ matures in $1$ year.

a$.$ What will the value of the Bond $L$ be if the going interest rate is $5\%,7\%,$ and $12\%?$ Assume that only one more interest payment is to be made on Bond $S$ at its maturity and that $11$ more payments are to be made on Bond L$.$ Round your answers to the nearest cent.

b$.$ Why does the longer$-$term bond's price vary more than the price of the shorter$-$term bond when interest rates change?

I. Long$-$term bonds have lower reinvestment rate risk than do short$-$term bonds.

II$.$ The change in price due to a change in the required rate of return increases as a bond's maturity decreases.

III. Long$-$term bonds have greater interest rate risk than do short$-$term bonds.

IV$.$ The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

V$.$ Long$-$term bonds have lower interest rate risk than do short$-$term bonds.