P1.1 Sonia Gomez, a 45-year-old woman, wishes to accumulate $250 000 over the next 15 years to supplement her superannuation savings. 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% ordinary shares and 50% bonds.

Sonia 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 the Appendix to Chapter 4). Her financial adviser indicated that for every $1000 Sonia 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 the time-value techniques that are described in the Appendix to Chapter 4.) Sonia plans to accumulate needed funds by making equal, annual, end-of-year investments over the next 15 years.

a. How much money does Sonia need to accumulate by making equal, annual, end-ofyear investments to reach her goal of $250 000?

b. How much must Sonia deposit annually to accumulate at the end of year 15 the sum calculated in part a?