Mini Case $$ Assignment $1$

Carolyn Bowen, who just turned $55,$ is employed as an administrative assistant for the Xcon Corporation,

where she has worked for the past $20$ years. She is in good health, lives alone, and has two grown

children. A few months ago her husband died, leaving her with only their home and the proceeds from a

$$75,000$ life insurance policy. After she paid medical and funeral expenses, $$60,000$ of the life insurance

proceeds remained. In addition to the life insurance proceeds, Carolyn has $$37,500$ in a savings account,

which she had accumulated over the past $10$ years. Recognizing that she is within $10$ years of retirement,

Carolyn wishes to invest her limited resources so she will be able to live comfortably once she retires.

Carolyn is quite superstitious. After consulting with a number of psychics and studying her family tree,

she is certain she will not live past $80.$ She plans to retire at either $62$ or $65,$ whichever will allow her to

meet her long$-$run financial goals. After talking with a number of knowledgeable individuals$-$including, of

course, the psychics$-$Carolyn estimates that to live comfortably in retirement, she will need $$45,000$ per

year before taxes. This amount will be required annually for $18$ years if she retires at $62$ or for $15$ years if

she retires at $65.$ As part of her financial plan, Carolyn intends to sell her home at retirement and rent an

apartment. She has estimated that she will net $$112,500$ if she sells the house when she is $62$ and

$$127,500$ if she sells it when she is $65.$ Carolyn has no financial dependents and is not concerned about

leaving a sizable estate to her heirs.

If Carolyn retires at age $62,$ she will receive from Social Security and an employer$-$sponsored pension

plan a total of $$1,359$ per month $($$$16,308$ annually$)$; if she waits until age $65$ to retire, her total retirement

income will be $$1,688$ per month $($$$20,256$ annually$).$ For convenience, Carolyn has already decided to

convert all her assets at the time of retirement into a stream of annual income and she will at that time

purchase an annuity by paying a single premium. The annuity will have a life just equal to the number of

years remaining until her $80$th birthday. If Carolyn retires at age $62$ and buys an annuity at that time, for

each $$1,000$ that she puts into the annuity she will receive an annual benefit equal to $$79$ for the

subsequent $18$ years. If she waits until age $65$ to retire, each $$1,000$ invested in the annuity will produce

an annual benefit of $$89\mathrm{.}94$ for the $15$ years.

Carolyn plans, to place any funds currently available into a savings account paying $6\%$ compounded

annually until retirement. She does not expect to be able to save or invest any additional funds between

now and retirement.

Questions

a$.$ Assume that Carolyn places currently available funds in the savings account. Determine the

amount of money Carolyn will have available at retirement once she sells her house if she retires

at $(1)$ age $62$ and $(2)$ age $65.$

b$.$ What is the annual rate of return she earns on the annuities?

c$.$ Using the results from a$,$ determine the level of annual income that will be provided to Carolyn

through purchase of an annuity at $(1)$ age $62$ and $(2)$ age $65.$

d$.$ With the results found in the preceding questions, determine the total annual retirement income

Carolyn will have if she retires at $(1)$ age $62$ and $(2)$ age $65.$

e$.$ From your findings, do you think Carolyn will be able to achieve her long$-$run financial goal by

retiring at $(1)$ age $62$ or $(2)$ age $65?$ Explain.

f$.$ Evaluate Carolyn's investment plan in terms of her use of a savings account and an annuity rather

than other investments. Comment on the risk and return characteristics of her plan. What

recommendations might you offer Carolyn? Be specific.

Instructions:

Please submit a typed report answering all the questions.

Show all the calculations clearly.