A woman deposits $13,000 at the end of each year for 9 years in an investment account with a guaranteed interest rate of 5% compounded annually. (a) Find the value in the account at the end of the 9 years. (b) Her sister works for an investment firm that pays 4% compounded annually. If the woman deposits money with this firm instead of the one in part (a), how much will she have in her account at the end of 9 years? (c) How much would she lose or gain over 9 years by investing in her sister's firm?