$1.)$ Sara and Sylvie have found a small house in the St$.$ Norbert neighbourhood of Winnipeg. They can buy the house for $$179900.$After negotiating with their bank, they have been offered a mortgage for $90\%$ of the cost at $4\mathrm{.}5\%$ compounded semi$-$annually, with regular weekly payments for $15$ years.

a$)$ How much will the down payment be$?$

b$)$ How much will the principal of the mortgage be$?$

c$)$What will the regular payment amount be$?$

d$)$How long will it take before they have paid off half the loan?

e$)$ How much interest will they pay in all

$2.)$ Lissa, the owner of a health food store, was advanced $$15000$ by an investor. She signed a promissory note that stated the conditions of the loan: interest will accumulate at a rate of $2\mathrm{.}6\%,$ compounded quarterly, and payments of $$1200$ will be made at the end of every$3-$month period.

a$)$ How long will it take Lissa to repay her investor?

b$)$ How much interest will Lissa pay?