Funding Jill Moran's Retirement Annuity

Sunrise Industries wishes to accumulate funds to provide a retirement annuity for its vice president of

research, Jill Moran. Ms$.$ Moran, by contract, will retire at the end of exactly $12$ years. Upon retirement, she

is entitled to received an annual end$-$of$-$year payment of $$42,000$ for exactly $20$ years. If she dies prior to

the end of the $20-$year period, the annual payments will pass to her heirs. During the $12-$year "accumulation

period," Sunrise wishes to fund the annuity by making equal, annual, end$-$of$-$the deposits into an account

earning $9\%$ interest. Once the $20-$year "distribution period" begins, Sunrise plans to move the accumulated

monies to an account earning a guaranteed $12\%$ per year. At the end of the distribution period, the account

balance will equal zero. Note that the first deposit will be made at the end of year $1$ and that the first

distribution payment will be received at the end of year $13.$

TO DO

How large a sum must Sunrise accumulate by the end of year $12$ to provide the $20-$year, $$42,000$

annuity?

How large must Sunrise's equal, annual, end$-$of$-$year deposits into the account be over the $12-$year

accumulation period to fund fully Ms$.$ Moran's retirement annuity?

How much would Sunrise have to deposit annually during the accumulation period if it could earn $10\%$

rather than $9\%$ during the accumulation period?

How much would Sunrise have to deposit annually during the accumulation period if Ms$.$ Moran's