now consider the second alternative$-$five annual payments of $$2,000$ each. Assume that the payments are made at the end of each year.

a$.$ what type of annuity is this?

b$.$ what is the future value of this annuity if the payments are invested in an account gpaying $10$ percent interest annually?

c$.$ what is the future value if the payments are invested with the first national bank, which offers semiannual compounding?

d$.$ what size payment would be needed to accumulate $$20,000$ under annual compounding at a $10$ percent interest rate?

e$.$ what lump sum, if deposited today, would produce the same stream of payments as in part b$?$

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