PLP Industries wishes to accumulate funds to provide a retirement annuity for its vice-president of research, Jane Magnan. Ms. Magnan will retire in exactly 12 years' time. Upon retirement, she is entitled to receive an annual end-of-year payment of $52,000 for 20 years. During the 12-year "accumulation period," PLP wishes to fund the annuity by making equal annual end-of-year deposits into an account earning a return of 9.64 percent compounded quarterly. Once the 20-year "retirement period" begins, PLP plans to move the accumulated monies into a safer investment account that is expected to earn 7 percent per year. At the end of the 20-year retirement period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13. a) How large a sum must PLP accumulate by the end of year 12 to provide the 20-year, $52,000 annuity? (4 points) b) If the interest rate was 7 percent compounded monthly (but everything else is the same) would your answer in (a) be larger or smaller? Why? Note: you do not need calculations for this answer. (2 points) c) How large must PLP's equal annual end-of-year investments into the account be over the 12-year accumulation period to fund fully Ms. Magnan's retirement annuity? (4 points) d) How much would PLP have to invest annually during the accumulation period if Ms. Magnan's retirement annuity was a perpetuity and all other terms were the same as initially described? (3 points) e) Ms. Magnan sets herself a goal of amassing $1 million in her retirement account by the time she retires. In addition to PLP's annual contributions, Ms. Magnan contributes to the account $500 every month over the 12-year accumulation period (starting one month from now). Also, she expects to receive a $15,000 bonus 4 years from now which she will also put into her retirement account. Will Ms. Magnan be able to achieve

PLP Industries wishes to accumulate funds to provide a retirement annuity for its vice-president of research, Jane Magnan. Ms. Magnan will retire in exactly 12 years' time. Upon retirement, she is entitled to receive an annual end-of-year payment of $52,000 for 20 years. During the 12 -year "accumulation period," PLP wishes to fund the annuity by making equal annual end-of-year deposits into an account earning a return of 9.64 percent compounded quarterly. Once the 20 -year "retirement period" begins, PLP plans to move the accumulated monies into a safer investment account that is expected to earn 7 percent per year. At the end of the 20 -year retirement period, the account balance will equal zero. Note that the first deposit will be made at the end of year 1 and the first distribution payment will be received at the end of year 13 . a) How large a sum must PLP accumulate by the end of year 12 to provide the 20 -year, $52,000 annuity? (4 points) b) If the interest rate was 7 percent compounded monthly (but everything else is the same) would your answer in (a) be larger or smaller? Why? Note: you do not need calculations for this answer. ( 2 points) c) How large must PLP's equal annual end-of-year investments into the account be over the 12 -year accumulation period to fund fully Ms. Magnan's retirement annuity? (4 points) d) How much would PLP have to invest annually during the accumulation period if Ms. Magnan's retirement annuity was a perpetuity and all other terms were the same as initially described? (3 points) e) Ms. Magnan sets herself a goal of amassing $1 million in her retirement account by the time she retires. In addition to PLP's annual contributions, Ms. Magnan contributes to the account $500 every month over the 12-year accumulation period (starting one month from now). Also, she expects to receive a $15,000 bonus 4 years from now which she will also put into her retirement account, Will Ms. Magnan be able to achieve