You are considering purchasing a car from a local car dealer with an MSRP $($manufacturer$\text{'}$s suggested

retail price$)$ of $$30,000.$ Since you don't have enough cash to pay in full, you're considering opting for the

dealer's "deferred payment plan"$-$ you pay the dealer $$5,000$ cash today and a payment of $$1,050$ at the

end of each of the next $30$ months.

Question:

$1.$ Assumming that $15\%$ is the annual opportunity cost $($a local bank is willing to give you a car loan

at the annual rate of $15\%),$ calculated the present value of all the payments on the dealer$$s

deferred payment plan.

$2.$ What is the effective annualized interest rate being charged by the dealer $($IRR$)?$