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Let's suppose you are going to borrow $10,000 on October 1, 2017. You have two re-payment options:

1.     Let's suppose you are going to borrow $10,000 on October 1, 2017. You have two re-payment options:
(i)               you promise to repay $1,000 every year on October 1 for four years (so, on 10/1/2018; 10/1/2019; 10/1/2020; and 10/1/2021) and repay the $10,000 principal on October 1, 2021.
(ii) you promise to repay $1,000 every year on October 1 for ten years (so, on 10/1/2018; 10/1/2019; 10/1/2020, 10/1/2021 etc. out to 10/1/2027) and repay the $10,000 principal on October 1, 2027.
The interest rate on similar loans is 10% annually and expected to stay at 10% per year for at least the next ten years.
(A) Which alternative (i) or (ii) has the lowest present value, thus costs you the least in terms of present value? Please show your work.
(B) Suppose interest rates suddenly fall from 10% to 5% (and are expected to stay at the new lower rate for at least 10 years) just after you make your agreement. If you could, would you wish to change the option you chose? Why or why not? Please explain.
(C) Suppose interest rates suddenly rise from 10% to 15% (and are expected to stay at the new higher rate for at least 10 years) just after you make your agreement. If you could, would you wish to change the option you chose? Why or why not? Please explain.
(D) Let's suppose you chose option (ii) when interest rates were 10% (and expected to stay there). Someone says to you: "You could save $6000 in interest payments if you paid back the loan in four years rather than ten years. Why didn't you do that?" What's your answer? 

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