Patty Scheme lenberg, a 45-year-old woman, wishes to accumulate $300,000 over the next 15 years to supplement the retirement programs that are being funded by the federal government and her employer. She expects to earn an average annual return of about 8% by investing in a low-risk portfolio containing about 20% short-term securities, 30% common stock, and 50% bonds. Patty currently has $31,500 that at an 8% annual rate of return will grow to about $100,000 at the end of 15 years (found using time-value techniques that will be described in Chapter 4’s appendix). Her financial adviser indicated that for every $1,000 Patty wishes to accumulate at the end of 15 years, she will have to make an annual investment of $36.83. (This amount is also calculated on the basis of an 8% annual rate of return using time-value techniques that are described in Chapter 4’s appendix.) Patty plans to accumulate needed funds by making equal, annual, end-of-year investments over the next 15 years. a. How much additional money does Patty need to accumulate over time to reach her goal of $300,000? b. How much must Patty deposit annually to accumulate the sum calculated in part a over the next 15 years?