### Author Topic: Math Problem  (Read 4704 times)

#### BuzzardsBay

• Posts: 81
##### Math Problem
« on: September 26, 2013, 08:23:11 AM »
If I want to have a total stash of \$800,000 and I currently have about \$150,000 I will obviously need the difference of \$650,000.  But I don't need to save the whole 650 because what I already have invested is growing and earning money and will continue to do so as I add to it.

So if I use a 5 year time frame (or 7 or 10), how do I figure out how much I have to save over the next 5 years?  Is there some kind of formula I can use and plug in different interest rates and different time frames? I'm sure there must be, but I have no idea where to begin.

I was thinking about it this morning and I would love to see an actual estimated number.  I think it will make it much more "real" and it will feel much more attainable than just looking at the amount of \$650,000.  Plus, I tend to save so much more when I have a number or goal to work towards each year.

Thanks for your help.  I love this site and the forums!

#### matchewed

• Magnum Stache
• Posts: 4388
• Location: CT
##### Re: Math Problem
« Reply #1 on: September 26, 2013, 08:33:32 AM »
Networthify.com

Go to the retirement calculator.

You can play with some numbers there. It's a good but simple tool.

#### Half-Borg

• Bristles
• Posts: 272
##### Re: Math Problem
« Reply #2 on: September 26, 2013, 08:34:50 AM »
Invest 1000 per year for 6% for 5 years:

1000 invested for 5 years = 1000*1.06^5
1000 invested for 4 years = 1000*1.06^4
1000 invested for 3 years = 1000*1.06^3
1000 invested for 2 years = 1000*1.06^2
1000 invested for 1 years = 1000*1.06^1

1000 * (1.06^5+1.06^4+1.06^3+1.06^2+1.06^1)

Figuring out a more flexible formula is for the next guy ;)

#### tooqk4u22

• Magnum Stache
• Posts: 2532
##### Re: Math Problem
« Reply #3 on: September 26, 2013, 08:45:15 AM »
In addition to the websites you can also do this on excel using the PMT formula.

#### mpbaker22

• Handlebar Stache
• Posts: 1095
##### Re: Math Problem
« Reply #4 on: September 26, 2013, 08:58:50 AM »
I prefer to just use excel basic calculations.  A1 = 150,000, A2 = (A1 times C1)+B2.  B2 = savings for year 2.  C1 = investment rate of return.
Using the dollar signs around C1 allows you to drop down the formula in A2 and B2, and allows for more manual manipulation to see how different things affect it.

Just my personal preference.

#### tooqk4u22

• Magnum Stache
• Posts: 2532
##### Re: Math Problem
« Reply #5 on: September 26, 2013, 09:05:12 AM »
Just remember that \$800k tomorrow is not equal to \$800k today - so if you think you need \$800k today then you need to adjust for inflation. A simple but not precise way to do it is to take 3% off of your expected annual return.

Example - I expect a 7% average return so I would plug 4% into the calculator to adjust for inflation.

#### Insanity

• Handlebar Stache
• Posts: 1025
##### Re: Math Problem
« Reply #6 on: September 26, 2013, 09:40:45 AM »
Networthify.com

Go to the retirement calculator.

You can play with some numbers there. It's a good but simple tool.

There seems to be an issue with this site.. Somehow if my WDR is higher than my Return rate I can retire sooner???

#### aclarridge

• Guest
##### Re: Math Problem
« Reply #7 on: September 26, 2013, 09:57:35 AM »
Here's a simple calculator that you can play around with. An inflation-adjusted ~50k per year should do the trick in 10 years.

#### happy

• Walrus Stache
• Posts: 7093
• Location: NSW Australia
##### Re: Math Problem
« Reply #8 on: September 26, 2013, 10:01:43 AM »
My math is a bit rusty so I'd use my fave compound calculator and start pluggin g in numbers:

http://jaw.iinet.net.au/stuff/interest.html

using Jaws calc, starting with 150k, at 7%interest, you would need to save \$8k a month for 5 years to get \$786k

Feed some different numbers in to run different scenarios

#### Posthumane

• Bristles
• Posts: 318
• Location: Alberta
##### Re: Math Problem
« Reply #9 on: September 26, 2013, 10:08:53 AM »
What you are looking for is the Future Value (FV) formula, as applied to a fixed present value and an annual annuity.
http://en.wikipedia.org/wiki/Future_value
So first off the future value of your 150k in 5 years with 4% real returns is 150k * 1.04^5 = \$182497.94. So what you need to save from your annual payments is 617502.06.

The formula for the annuity is listed near the bottom of that wikipedia page. Solve for payment amount:
PmntAmt = (FV*r)/([1+r]^n - 1)  where r is the rate of return and n is the number of compounding periods.

FV = 617502.06
n = 5 (assuming annual compounding)
r = 0.04 (7% nominal returns - 3% inflation)
Payment Amount = 114007.62
So, as you can see, over a short 5 year time period the compound interest doesn't give you a huge boost. If you rework the numbers for 10 years it looks like this:
FV(150k) = 150k*(1.04^10) = 222036.64
FV(required from payments) = 577963.36
PmntAmt = \$48139.11

#### BuzzardsBay

• Posts: 81
##### Re: Math Problem
« Reply #10 on: September 26, 2013, 10:13:13 AM »
Yes - Future Value.  That's it.  I new I had learned something in school that would give me a formula to use, but I had no clue what it was.

And the websites and other things people have posted are great.  I'm going to have fun playing with this.

Thank you all.  You guys are awesome!

#### AlmostIndependent

• Pencil Stache
• Posts: 521
• Age: 40
• Location: Anchorage, AK
##### Re: Math Problem
« Reply #11 on: September 26, 2013, 02:03:48 PM »
For savings and investment growth I really like this calulator.

http://personal.fidelity.com/toolbox/growth/growth.shtml