You are considering the purchase of two $$1,000$ bonds, both issued by Dalton Mining Company. Your expectation is that interest rates will drop and you want to buy the bond which provides the maximum capital gains potential. The first Dalton bond has a coupon rate of $6$ percent with four years to maturity, while the second has a coupon rate of $14$ percent and comes due five years from now. The market rate of interest $($discount rate$)$ is $8$ percent. Show work for partial credit.

a$.$ What is the price and duration of the first Dalton Bond?

Price $=$

Duration $=$

b$.$ What is the price and duration of the second Dalton Bond?

Price $=$

Duration $=$

c$.$ You expect interest rates to go to $10\%.$ What is the new price of the first Dalton Bond?

Price $=$

d$.$ Interest rate is $10\%.$ Which Bond do you choose and why? $($tip: you decide future interest rates.$)$

e$.$ What happened to duration because of the new interest rate going to $10\%,$ and why