Use the following information to answer the questions below.

ABC Life Insurance Company is issuing a Single$-$Premium Deferred Equity$-$Linked Annuity with the following

characteristics:

Annuity Premium

Guaranteed Minimum Crediting Rate

Annuity Maturity

$$450,000$

$2\mathrm{.}50\%$

$11$ Years

Other Pertinent Data:

Current Level of S&P $500$ Index

Price of At$-$The$-$Money S&P $500$ Index Call Option

With $11$ Year Maturity

Current Rate on $11-$Year, Zero Coupon Corporate Bond

a$.$ How much should the insurance company purchase in zero$-$coupon bonds today to be able to meet the

guaranteed minimum rate?

b$.$ How many S&P $500$ Index Call Options should the company purchase today?

c$.$ Complete the table below for values and returns $11$ years from now. Show all of your work.

d$.$ Draw a graph with axis well labeled comparing the Equity$-$Linked Annuity returns to the stock market

returns.Use the following information to answer the questions below.

ABC Life Insurance Company is issuing a Single$-$Premium Deferred Equity$-$Linked Annuity with the following

characteristics:

Annuity Premium

Guaranteed Minimum Crediting Rate

Annuity Maturity

$$450,000$

$2\mathrm{.}50\%$

$11$ Years

Other Pertinent Data:

Current Level of S&P $500$ Index

Price of At$-$The$-$Money S&P $500$ Index Call Option

With $11$ Year Maturity

Current Rate on $11-$Year, Zero Coupon Corporate Bond

a$.$ How much should the insurance company purchase in zero$-$coupon bonds today to be able to meet the

guaranteed minimum rate?

b$.$ How many S&P $500$ Index Call Options should the company purchase today?

c$.$ Complete the table below for values and returns $11$ years from now. Show all of your work.

d$.$ Draw a graph with axis well labeled comparing the Equity$-$Linked Annuity returns to the stock market

returns.