Melissa Chung, a $24-$old, single, healthy female has just opened an HSA in conjunction with a qualified HDHP$.$ She wants to determine how much the account might be worth if he funds the HSA primarily for retirement purposes.$$

a$.$ How much will the account be worth at age $67$ if Melissa makes a deposit of $$4,000$ per year for the next $10$ years before changing to his employer$$s standard health plan because of family health concerns and discontinuing contributions to the HSA? Assume that Melissa earns $6$ percent per year for the $10$ years while she might need the money, but after she changes plans $($and increases her risk tolerance$),$ the return will be $8$ percent annualized.$$

b$.$ How much will the account be worth at age $67$ if Melissa makes the maximum deposit of $$4,000$ per year for the next $10$ years, but also takes a $$6,000$ qualified distribution at age $30?$ Assume Melissa earns $3$ percent per year for the next $10$ years while she might need the money, but after she changes plans the return will be $7$ percent annualized.$$

c$.$ If Melissa takes a $$15,000$ nonqualified distribution from her HSA prior to age $63,$ how much in federal income tax and penalties will she owe? Assume that she is in the $22$ percent marginal tax bracket.