Question

(Compounding using a calculator and annuities due ) Springfield mogul Montgomery Burns, age 90, wants to retire at age 100 in order to steal candy from babies full time. Once Mr. Burns retires, he wants to withdraw $0.9 billion at the beginning of each year for 6 years from a special offshore account that will pay 22 percent annually. In order to fund his retirement, Mr. Burns will make 10 equal end-of-the-year deposits in this same special account that will pay 22 percent annually. How much money will Mr. Burns need at age 100, and how large of an annual deposit must he make to fund this retirement account?

a. How much money will Mr. Burns need when he retires?

Answer: $ _________billion. (Round to three decimal places.)

b. How large of an annual deposit must he make to fund this retirement account?

Answer: $ __________million. (Round to two decimal places.)

Answer 1

Present Value Annuity Due =

where r is the rate of Return for compounding period = 22%

n is the no of compounding period 6 years

=

= 3477275.78545

Future Value Annuity =

r = 0.22

n = 10

3477275.78545 =

3477275.78545 = Periodic Payment * 28.6574155245

Periodic Payment = 3477275.78545 / 28.6574155245

Periodic Payment = 121339.49

Answer a)

Answer in Billions = 3477275.78545 / 1,000,000,000 = 0.0035 billion

Answer b)

Answer in millions = 121339.49 / 1000,000 = 0.1213 millions