   City-Data Forum Stupid math question
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 Location: San Jose, CA 1,318 posts, read 3,165,562 times Reputation: 760

Quote:
 Originally Posted by Giesela Having a 401k for retirement is really bad for those of us who just don't get math and never will. So...if someone invested 70,000 and 5 years later had 100,000 for a total gain of 30,000 over 5 years what is that in a percentage? .428? so is that less than 1% gain? I.e. i'd be better off with my 401K money in a CD?
I wouldn't say it is a stupid question.
To get the total return on investment you must take (current value/ starting value) -1, (100 000 / 70 000) - 1 = 0.428571429, once you get a decimal value to change it to percentage terms you must multiply by 100.
0.428571429 * 100 = 42.85%.

To get the annualized rate of return you must use the following formula:
(current value/ starting value)^(1/# of years) -1. The ^ symbol means it is an exponent, you don't need to remember algebra or anything, you can just plug it in to google, it will calculate it for you.
((100 000 / 70 000)^(1 / 5)) - 1 = 0.0739409238 = 7.39%

In order to do better with a 5 yr CD you must get a rate better than 7.39%.

If you're starting from the APY advertised on a CD to get how much money you will get when the CD matures you need the following
(starting value)*(1+(APY %)/100)^(# of years).

For example you put \$1000 in a 4.15% 5-year CD how much money will you have when the CD matures.
1 000 * ((1 + (4.15 / 100))^5) = 1 225.45219 = \$1,225.45. There are lots of stuff mentioned in the article about Compound interest - Wikipedia, the free encyclopedia, but I usually only remember the 3 formulas I listed here, and remember to use the advertised APY instead of the advertised APR to do these calculations.

If you want to know why the formula (starting value)*(1+(APY %)/100)^(# of years) works, you have to remember that the APY is ALL the interest they give you in 1 year, including all their little calculations from APR. So the interest they give you is

APY/100 * starting value = interest @ year 1
starting value@ year 2 = starting value + interest @ year 1 (That should be easy to understand)
starting value@ year 3 = starting value@ year 2 + interest @ year 2
starting value@ year 4 = starting value@ year 3 + interest @ year 3
.
.
.
And so on.
starting value@ year 2 = starting value + interest @ year 1 = starting value + (APY/100 * starting value) = starting value * (1+(APY/100)), (I took out the common factor to the front)

starting value@ year 3 = starting value@ year 2 + interest @ year 2
starting value@ year 2 + APY/100 * starting value@ year 2
(starting value@ year 2)* (1+(APY/100))
= starting value * (1+(APY/100)) * (1+(APY/100)) (Substitute in the starting value@ year 2 you know from before)
= starting value * (1+(APY/100))^2

If you continue this for the 3rd year you can see the pattern. Basically every year the value multiplies itself by (1+(APY/100)), and continues to grow like that.

I basically try to remember those 3 formulas, and that usually helps me get answers to most of my investment questions. Like if I have \$10,000 and I want to have \$20,000 in 10 years without investing anything more, what interest rate do I need. (current value/ starting value)^(1/# of years) -1 =
((20 000 / 10 000)^(1 / 10)) - 1 = 0.0717734625 = 7.18% or 7.2% roughly.
That also reminds me of a shorthand way to figure out when and investment will double in value: Rule of 72 - Wikipedia, the free encyclopedia.

Well best of luck, it is a lot to take in, but you don't have to remember the details, I usually just remember the 3 formulas.   Location: Mississippi 114 posts, read 388,385 times Reputation: 82
You could just go here and enter your data.
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