Retirement Calculator

  • Thread starter brian110872
  • Start date
  • Tags
    Calculator
In summary, the conversation is about a chart on a bank website that calculates the amount of money needed to withdraw $30,000 per year from savings. The calculation assumes a 7.5% annual interest rate and a 5-year withdrawal period. The end balance is calculated by starting with the initial amount and adding interest, then subtracting the amount withdrawn. The pattern is repeated for each year until the final balance is reached. The final balance is calculated by solving the equation 1.0755X= 30000(5.808), resulting in an approximate value of $130,480. The conversation also includes a discussion on the accuracy of the calculation and the use of a mathematical software called Mathematica.
  • #1
brian110872
4
0
On this chart:
http://www.banksite.com/calc/retire?with=30000&lngt=5&lngt=5&pay2=0.0&intr=7.5&outt=HTML+Tables [Broken]
how did they calculate 130479.79? I know how they got the "Interest" and "End Bal" just not the 130479.79. Anyone have any suggestions?
Here is the original form:
http://www.banksite.com/calc/retire [Broken]

Thank You,
Brian
 
Last edited by a moderator:
Mathematics news on Phys.org
  • #2
In this example, the objective is to be able to withdraw $30,000 per year from savings. It assumes 7.5% interest (it's obviously very old!). The "end balance" is, of course,0 by definition.

Suppose you had X dollars in the bank, drawing 7.5% simple interest.
After 1 year, before you withdraw anything, you would have the original X plus interest, (0.075)(30000) or a total of (1+ 0.075)X= 1.075X. Now, you withdraw 30000. You have 1.075X- 30000 left.

For the second year, repeat that with initial amount 1.075X-30000. Before withdrawing anything, but including interest, you would have
1.075(1.075X- 30000)= (1.075)2X- (1.075)(30000). After withdrawing your 30000 you will have (1.075)2X- (1.075)(30000)- 30000 left.

For the third year, you are starting with that amount so, before withdrawal you would have 1.075((1.075)2X- 1.075(30000)- 30000)= 1.0753X- 1.0752300000- 1.075(30000). Now withdraw 30000 from that: 1.0753X- 1.0752300000- (1.075)30000- 30000= 1.0753X- 30000(1+ 1.075+ 1.0752.

Do you see the pattern? After n years you will have 1.075nX- (30000)(1+ 1.075+ ...+ 1.075n-1. In particular, after 5 years you would have 1.0755X- (30000)(1+ 1.075+ 1.0752+ 1.0753+ 1.0754. Since in this example you are apparently only expecting to die 5 years after retirement, after 5 years, the "final balance" is to be 0. It's not that hard to calculate that 1+ 1.075+ 1.0752+ 1.0753+ 1.0754= 5.808 approximately. Solve the equation 1.0755X= 30000(5.808). I get slightly less than 130480. Try deducting the 30000 before adding the interest. That would be the same as replacing X by X-30000.
 
  • #3
Thanks for the reply HallsofIvy. For 1.075^5(X)= 30000(5.808), I'm getting X=121368. How am I miscalculating?
 
  • #4
brian110872 said:
Thanks for the reply HallsofIvy. For 1.075^5(X)= 30000(5.808), I'm getting X=121368. How am I miscalculating?
You're not, you've solved for x almost perfectly, actually your missing a few decimal places there, can I assume you are using mathematica?
 
  • #5
Zurtex said:
You're not, you've solved for x almost perfectly, actually your missing a few decimal places there, can I assume you are using mathematica?
What is mathematica?
 
  • #6
HallsofIvy,
I'm not sure how you got 130480 from 1.0755X= 30000(5.808).

Thank You,
Brian
 

What is a retirement calculator?

A retirement calculator is a tool that helps individuals estimate how much money they will need to save for retirement and how much they can expect to receive in retirement income.

How does a retirement calculator work?

A retirement calculator uses various inputs such as current age, retirement age, expected retirement income, and savings to project a person's retirement savings and income. It also takes into account factors like inflation and investment returns to make the projections more accurate.

Is a retirement calculator accurate?

A retirement calculator can provide a good estimate of retirement savings and income, but it is not a guarantee. It is important to regularly review and adjust the inputs and assumptions used in the calculator to reflect changes in your financial situation.

Do I need to use a retirement calculator?

While it is not necessary to use a retirement calculator, it can be a helpful tool in planning for retirement. It can give you a better understanding of your financial needs in retirement and help you make informed decisions about saving and investing.

Are there different types of retirement calculators?

Yes, there are various types of retirement calculators that cater to different needs. Some calculators focus on specific retirement plans, like 401(k) or IRA, while others provide a more comprehensive analysis of a person's retirement savings and income. It is important to choose a calculator that best suits your needs and goals.

Similar threads

Replies
9
Views
2K
Replies
0
Views
7K
  • Classical Physics
2
Replies
61
Views
954
Replies
1
Views
980
  • MATLAB, Maple, Mathematica, LaTeX
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
14
Views
1K
Replies
1
Views
1K
  • General Math
Replies
1
Views
2K
  • Aerospace Engineering
Replies
2
Views
6K
  • Introductory Physics Homework Help
Replies
9
Views
1K
Back
Top