Ivan has $$15,000$ in her savings account that pays interest at the effective rate of $5\%,$

compounded annually. At the end of each year, Ivan withdraws the interest earned that year and extra

cash $$1,000$ from the savings account. Then he invests them into Fund X that has an annual effective

rate of $10\%.$

$($a$)$ What is the remaining balance in Ivan$$s savings account after the withdrawal is made at the end of $10$ years?

$($b$)$ What is the total balance of Fund X at the end of $10$ years?