The Howe family recently bought a house. The house has a $30-$year,

$$241,644\mathrm{.}00$ mortgage with monthly payments and a nominal interest rate of

$4\mathrm{.}9$ percent. What is the total dollar amount of principal the family will pay

during the first $4$ years of their mortgage? $($Assume that all

payments are made at the end of the month.$)$

$$19,647\mathrm{.}91$

$$16,647\mathrm{.}91$

$$18,647\mathrm{.}91$

$$15,647\mathrm{.}91$

$$17,647\mathrm{.}91$A baseball player is offered a $5-$year contract that pays him the following amounts:

Year $1$: $$2\mathrm{.}9$ million

Year $2$: $$1\mathrm{.}3$ million

Year $3$: $$2\mathrm{.}4$ million

Year $4$: $$2\mathrm{.}5$ million

Year $5$: $$1\mathrm{.}4$ million

Under the terms of the agreement all payments are made at the end of each year.

Instead of accepting the contract, the baseball player asks his agent to negotiate

a contract that has a present value of $$2$ million more than that which has been

offered. Moreover, the player wants to receive his payments in the form of a $5-$year

annuity due. All cash flows are discounted at $10\mathrm{.}7$ percent. If the team were

to agree to the player's terms, what would be the player's annual salary $($in millions

of dollars$)?$

$$2\mathrm{.}52$

$$2\mathrm{.}72$

$$2\mathrm{.}42$

$$2\mathrm{.}82$

$$2\mathrm{.}62$