Calculate the following:

a$.$ What is the amount of the annuity purchase required

if you wish to receive a fixed payment of $$240,000$ for

$20$ years? Assume that the annuity will earn $7$ percent

per year.

b$.$ Instead of a lump sum, you wish to receive annuities

for the next $20$ years $($years $11$ through $30).$ What is the

constant annual payment you expect to receive at the

beginning of each year if you assume an interest rate of

$8$ percent during the distribution period

c$.$ Repeat parts $($a$)$ and $($b$)$ assuming earning rates of $7$ percent

and $9$ percent during the deposit period and earning rates

of $7$ percent and $9$ percent during the distribution period.

Please assist with excel working when solving. Thanks.