You deposit $$$$2$ comma $500$ at the end of the year $($kequals$0)$ into an account that pays interest at a rate of $7\%$ compounded annually. Upper A year after your$$ deposit, the savings account interest rate changes to $12\%$ nominal interest compounded monthly. Five years after your$$ deposit, the savings account again changes its interest$$ rate; this time the interest rate becomes $8\%$ nominal interest compounded quarterly. Nine years after your$$ deposit, the saving account changes its rate once more to $6\%$ compounded annually.

a$.$ How much money should be in the savings account $17$ years after the initial$$ deposit, assuming no further changes in the$$ account's interest$$ rate?

b$.$ What interest$$ rate, compounded$$ annually, is equivalent to the interest pattern of the saving account in Part$($a$)$ over the entire $17$ year$$ period?