PROBLEM $2(25$ MARKS$)$

You receive a credit card application from First Abu Dhabi Bank which offers a rate of $0\mathrm{.}5\%$ per year, compounded monthly for the first six months, increasing thereafter to $17\%$ compounded monthly. Assume that you transfer the $$6,000$ balance from your existing credit card and make no subsequent payments.

a$)$ What will the balance be at the end of the first six months? $(7$ marks$)$

b$)$ What will the balance be at the end of the first year? $(7$ marks$)$

c$)$ How much interest will you owe at the end of the first year? $(4$ marks$)$

d$)$ What effect will an increasing interest rate have on the interest amount you owe at the end of the year? $(7$ marks$)$