Question

Case:

You have just inherited a large sum of money and you are trying to determine how much you will get after retirement and how much you can spend now. For retirement you will deposit today (January 1,2015) 2,500,000 euros in a bank account paying 4.55% compounded annually. You do not plan on touching this deposit until you retire in five years (January 1, 2020) and you plan on living for 20 additional years and then drop dead on December 31, 2039.

During your retirement, you would like to receive income of 60,000 euros per year to be received the fist day of each year, with the first payment on January 1,2020, an the last payment on January 1, 2039. Complicating this objective is your desire to have one three-year fling, during which time you´d like to track down all the original members of Cold Play and get their autographs. To finance this, you want to receive additional 50,000 euros on January 1, 2035, 25,000 euros on January 1, 2036 and 8,000 euros on January 1, 2037.

Questions:

1.What will be your final savings balance by January 1, 2040?

2.What would be your final savings balance if you decided not to have the three-year fling ( without the 3 years of additional spending to get the autographs etc.) ?

Answer 1

Amount of deposit today on Jan1, 2015 = €2,500,000

Future Value of $2,500,000 after 5 years with interest at 4.55% compounded annually

= €2,500,000*(1+4.55%)^5 = €2,500,000*1.2491661= €3,122,915.22

Part 2:

Amount available after 20 years without the three-year fling = € 5,625,712.67   Calculated using FV function of Excel as follows:

Part 1:

Periodical withdrawals apart from the yearly amounts:

On Jan 1, 2035 (5 years before Jan 1, 2040)= €50,000

On Jan 1, 2036 (4 years before Jan 1, 2040)= €25,000

On Jan 1, 2037 (3 years before Jan 1, 2040)= €8,000

Future value of these amounts= 50,000*(1+4.55%)^5 + 25,000*(1+4.55%)^4 + 8,000*(1+4.55%)^3

= €62,458.30 + €29,870.06 + €9,142.44 = €101,470.80

Final savings without 3-year fling (as per part 2)= € 5,625,712.67   

Therefore, Final savings after the 3-year fling= € 5,625,712.67- 101,470.80= € 5,524,241.87