This problem demonstrates the dependence of the future value of an annuity on the number of payments. Suppose $1000 is invested at the end of each year. Assume the investments earn 5% compounded annually. Calculate the future value of the investments after each of the following numbers of payments:

a. 5

b. 10

c. 15

d. 20

e. 25

f. 30

Note that the future value increases proportionately more than n as n is increased.