Question

10) Part A. ?(Annuity payments) Lisa Simpson wants to have ?$1,600,000 in 60 years by making equal annual? end-of-the-year deposits into a? tax-deferred account paying 8.50 percent annually. What must? Lisa's annual deposit? be? (Round to the nearest? cent.)

Part B. (Present value of annuity? payments) The state? lottery's million-dollar payout provides for $1.4 million to be paid in 20 installments of ?$70,000 per payment. The first ?$70,000 payment is made? immediately, and the 19 remaining ?$70,000 payments occur at the end of each of the next 19 years. If 9 percent is the discount? rate, what is the present value of this stream of cash? flows? If 18 percent is the discount? rate, what is the present value of the cash? flows?? (Round to the nearest? cent.)

Answer 1

a.Future value of annuity=Annuity[(1+rate)^time period-1]/rate

1,600,000=Annuity[(1.085)^60-1]/0.085

1,600,000=Annuity*1559.919777

Annuity=(1,600,000/1559.919777)

=$1025.69(Approx).

2.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

At 9%:

Present value=$70,000+$70000[1-(1.09)^-19]/0.09

=$70000+$70000*8.950114779

=$696,508.03(Approx).

At 18%

Present value=$70,000+$70000[1-(1.18)^-19]/0.18

=$70000+$70000*5.316240867

=$442,136.86(Approx).