I need help with whole numbers with decimals to a power like 1.02 o the fourth power we need this for compound interest problem but the explanitions in the book are bad, thanks

When you need to raise a number such as 1.02 to a power, this is what you do:

Split the integer portion from the decimal portion. Square (or whatever it is) separately.

1^2 = 1

(0.02)^2 = (0.0004)
To do this, first multiple just the numbers: 2*2 = 4. Then count the total number of decimals:
0.02* 0.02 = 4 decimal places
Write the number (4) with that number of decimal places: 0.0004.

Put them back together: 1.0004

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Hi -

In your earlier post it was stated that (1.02)^2 results in 1.0004(using the method listed at the end of this post by MGMAT Staff) In reality (1.02)^2 = 1.0404. I am guessing that 1.0004 is an approximate calculate to arrive at 1.0404?

I was trying to do a compound interest problem where i had to calculate (1.02)^4

$5000 invested for 1 year at a rate of 8% compounded quartely will earn approximately what amount?

$5000 (1+0.08/4)^4 = $5000(1.02)^4 = $412

Calculating (1.02)^4 according to the method below would be 1.00000016
in reality (1.02)^4 = 1.08243216
What am i doing wrong?

How can i easily calculate 5000*(1.02)^4?
Is there is a shortcut method? The manual calculation will take well over 2 minutes.

MGMAT STAFF:
When you need to raise a number such as 1.02 to a power, this is what you do:

Split the integer portion from the decimal portion. Square (or whatever it is) separately.

1^2 = 1

(0.02)^2 = (0.0004)
To do this, first multiple just the numbers: 2*2 = 4. Then count the total number of decimals:
0.02* 0.02 = 4 decimal places
Write the number (4) with that number of decimal places: 0.0004.

Put them back together: 1.0004

You are entirely right! That is not correct.

However, I'm going to disagree that it takes so much time to calculate. I think that it is possible to do. I just timed myself taking 1.02^4 and it took 30 seconds, and I am a little rusty at longhand calculations.

The first thing I did was multiplied 1.02 * 1.02. I got 1.0404 like you said.

I then didn't even calculate out the second one. I knew it would be ugly. I think at this point you want to estimate that you have a little more than 1.04, squared.

One way I estimate something like 1.04 * 1.04 is to say:
I have 1* 1.04=1.04
Then I'm taking .04 of 1.04, so a little bit more than .04.
Together I have 1.08. That's close enough! You shouldn't have to do crazy math.

_________________
Jamie Nelson
ManhattanGMAT Instructor