Professor's Annuity Corp. offers a lifetime annuity to retiring professors. For a

payment of $$80,000$ at age $65,$ the firm will pay the retiring professor $$600$ a month

until death. If the professor's remaining life expectancy is $20$ years, what is the yearly

rate on this annuity?

You are $40$ years old and wish to retire at age $65.$ You expect to be able to average a

$6\%$ annual rate on savings over your lifetime. You would like to save enough money

to provide $$8,000$ per year beginning at age $66$ in retirement income to supplement

other sources $($social security, pension plans, etc.$).$ Suppose you decide that the extra

income need be provided for only $15$ years $($up to age $80).$

a$)$ How much will you have saved when you are $65$ to make this plan possible?

b$)$ How much must you save each year between now and retirement to achieve

your goal? Assume that your first contribution to the savings plan will take

place one year from now.

Your consulting firm produced cash flows of $$100,000$ this year and you expect cash

flow to keep pace with any increase in the general level of prices. The interest rate is

currently $6$ percent and you anticipate inflation of about $2$ percent.

a$)$ What is the present value of your firm's cash flow for years $1$ through $5?$

b$)$ How would your answer to a$)$ change if you anticipated no growth in cash flow?

Good news: You will almost certainly be a millionaire by the time you retire in $50$

years. Bad news: The inflation rate over your lifetime will average about $3$ percent.

a$)$ What will be the real value of $$1$ million by the time you retire in term's of

today's dollar?

b$)$ What real annuity $($in today's dollars$)$ will $$1$ million support if the real interest

rate is $2$ percent and the annuity must last for $20$ years?

Suppose that $5-$year government bonds are selling on a yield of $4$ percent.

a$)$ Value this bond with a $6$ percent annual coupon.

b$)$ What is the current yield of this bond?

c$)$ Suppose that one year later the bond still yields $4$ percent. What return has the

bond holder earned over the $12$ month period?

$($doing this in excel$)$