Goal $4$: Save $$15000$ in an account with $15\%$ for a down payment on a home in $6$ years. $($no additional payments$)$ How much must be deposited today in the account to reach this goal? Goal $5$: Open a Roth IRA at $5\%$ for $20$ years and contribute $$1500$ on a semi$-$annual basis. What is the potential balance of this account in $20$ years?