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Part $1$

Your friends are going to Puerto$$ Vallarta, Mexico, over Reading Week and you want to go too.$$ Unfortunately, you$$ haven't been good at$$ saving, so you need to borrow $$$$2300$ to pay for the trip. You can finance the trip on your credit card at a rate of $20\%$ APR with daily compounding.$$ Alternatively, your parents$($who are both$$ bankers$)$ are willing to lend you the money at a rate of $11\%$ per six months compounded every six months.

a$.$ What is the EAR of borrowing with your credit$$ card? $($Assume $365$ days in a$$ year.$)$

b$.$ What is the EAR of borrowing from your$$ parents?

c$.$ If you plan to repay the $$$$2300$ in equal monthly$$ instalments, what would be the rates to use in the following annuity formulas to calculate your monthly payments.

i$.$ Assume you borrowed with the credit card.

ii$.$ Assume you borrowed from your parents.

PV left parenthesis annuity of Upper C for n periods with interest rate r right parenthesis equals Upper C times StartFraction $1$ Over r EndFraction left parenthesis $1$ minus StartFraction $1$ Over left parenthesis $1$ plus r right parenthesis Superscript n EndFraction right parenthesis

$$or$$PV left parenthesis growing perpetuity right parenthesis equals StartFraction Upper C Over r minus g EndFraction