Question

Springfield mogul Montgomery​ Burns, age 75​, wants to retire at age 100 in order to steal candy from babies full time. Once Mr. Burns​ retires, he wants to withdraw ​$1 billion at the beginning of each year for 10 years from a special offshore account that will pay 27 percent annually. In order to fund his​ retirement, Mr. Burns will make 25 equal​ end-of-the-year deposits in this same special account that will pay 27 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?

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

Answer 1

PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	1000000000
r = the effective interest rate (also known as the discount rate)	27%
n = the number of periods in which payments will be made	10
PV of annuity at the time of retirement=	PMT x (((1-(1 + r) ^- n)) / r)
PV of annuity at the time of retirement=	1000000000* (((1-(1 + 27%) ^- 10)) / 27%)
PV of annuity at the time of retirement=	$      3,364,391,854
This retirement account will be funded with 25 annual payments so
FV of annuity
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	$      3,364,391,854
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	27%
n = the number of periods in which payments will be made	25
FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
3364391854	PMT x ((((1 + 27%) ^ 25) - 1) / 27%)
Annual payment required=	3364391854/ ((((1 + 27%) ^ 25) - 1) / 27%)
Annual payment required=	$        2,313,566.63