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

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.

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