A car dealership offers three different loan options for a five$-$year loan of $$20,000($i$.$e$.,$ you

borrow $$20,000$ today$).$ It charges an APR of $5\%,$ compounded semi$-$annually for all loans.

$($a$)$ One option is an interest$-$only loan. Write out the series of payments that you will make

over the course of the loan.

$($b$)$ The company also offers a discount loan. How much do you have to repay at the end of $5$

years?

$($c$)$ The third loan type is an amortizing loan with $10$ equal semi$-$annual payments. How

much would you pay every $6$ months?

$5.$ You currently have $$2,000$ in savings. You have a short$-$term job that pays $$1,000$ at the end

of each month for the next $9$ months. You are looking at renting an apartment. You will pay rent

at the beginning of each month. Assume the monthly EPR is $1\%.$ If you are renting for $12$

months, how expensive an apartment can you afford?