a$)$ Sandra wants to borrow $40,000$ for a

The lender offers her a choice of three payment structures:

i$)$ Pay all of the interest $(10\%$ per year$)$ and principal in one lump sum at the end of $5$ years

ii$)$ Pay interest at the rate of $10\%$ per year for $4$ years and then a final payment of interest and principal at the end of the $5$th year;

iii$)$ Pay $5$ equal payments at the end of each year inclusive of interest and part of the principal

Under which of the three options will Sandra pay the least interest and why? Calculate the to al amount of the payments and the amount of interest paid under each alternative