Question

Springfield mogul Montgomery Burns, age 80, wants to retire at age 100 so he can steal candy from babies full time. Once Mr. Burns retires, he wants to withdraw $500 million at the beginning of each year for 10 years from a special off-shore account that will pay 18% annually. In order to fund his retirement, Mr. Burns will make 20 equal end-of-the-year deposits in this same special account that will pay 18% annually. How large of an annual deposit must be made to fund Mr. Burns retirement plans

Answer 1

Answer:

Springfield mogul, Montgomery Burns

How large of an annual deposit must be made to fund Mr. Burns retirement plans:

= $94,644,751.67

Explanation:

a) Data and Calculations:

Age of Mr. Burns now = 80 years

Retirement age = 100 years

Annual withdrawal at the beginning of each year for 10 years = $500 million

Special offshore account pays interest = 18% annually

Investment for funding retirement:

Deposits = 20 equal end-of-the year deposits in the same special offshore account above.

b) Calculation of Future value of annual deposit after 20 years:

FV (Future Value) $13,877,572,093.01

PV (Present Value) $2,651,510,914.01

N (Number of Periods) 10.000

I/Y (Interest Rate) 18.000%

PMT (Periodic Payment) $500,000,000.00

Starting Investment $0.00

Total Principal $5,000,000,000.00

Total Interest $8,877,572,093.01

c) Calculation of Annual Deposit to reach the future value target of $13,833,567,810.87:

FV (Future Value) $13,877,567,810.87

PV (Present Value) $506,609,362.98

N (Number of Periods) 20.000

I/Y (Interest Rate) 18.000%

PMT (Periodic Payment) $94,644,751.67

Starting Investment $0.00

Total Principal $1,892,895,033.42

Total Interest $11,984,672,777.45

d) Mr. Burns will need to contribute $94,644,751.67 at the end of each period to reach the future value of $13,877,572,093.01.  Both the future value of deposits of $13,877,567,810.87  and the annual periodic payment of $94,644,751.67  are determined using online financial calculator.