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# how to figure (1+0.06) to the 5th

I know this isn't exactly an IT question, but I have to take this freakin financial mgt class on the way to an IT degree.
How do you calculate this
(1+0.06) with a tiny little 5 at the top of the right parentheses?

Thanks
dlewis61
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dlewis61
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1 Solution

Commented:
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Commented:

``````This is simple enough to do by hand:

1.06   x 1.06     =  1.1236        ==> Two  factors

1.1236 x 1.1236   =  1.26247696    ==> Four factors

1.06   x 1.1236   =                ==> Five factors
``````
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Commented:
>>  (1.06) x (1.06) x (1.06) x (1.06) x (1.06) =  1.33822558

The exact answer will have 10 decimal places.

If you invested \$1M for five years at 6% compounded annually, you would wind up with:

\$1,338,225.58       plus or minus fractions of a cent.
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Author Commented:
This is FANTASTIC
but how did you get the 1.06? Listen, I never got basic math skills....I got moved up to geometry etc. before I got all the basics down. I swear I'm not an idiot.

Any help you can render would be great
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Commented:
(1+0.06)^5 = (1+0.06) * (1+0.06) * (1+0.06) * (1+0.06) * (1+0.06)
Usually it is used in money and interest. For example: if you store USD 1000 to your bank and the bank gives you 6% interest annually, then your money will be USD 1000 * (1+0.06)^5 after 5 years = USD 1000 * (1+0.06) * (1+0.06) * (1+0.06) * (1+0.06) * (1+0.06) = USD 1338.2255776
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Commented:
(1+0.06)  really means (1.00 + 0.06), regular decimal addition.

This form: (1 + small value) probably means they want you to think about binomial
expansions and approximations.  Binomial mean two terms: the 1 and the 0.06.

http://en.wikipedia.org/wiki/Binomial_theorem
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Commented:
In scientific calculator, x^y means x raised to the yth power. It is usually written x with superscript y.
6^5 means you have to multiply 6 five times (6 * 6 * 6 * 6 * 6)
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Commented:
If you were taking a physics course d-glitch would be right. But since our course is in finance it is reasonable to thin the 1+0.06 = 1.06 (which as has been said is multiplied 5 times in your problem.
D-glitche's note is very interesting however (especially from the stand point of physics) His method is very good when dealing with number close to 1, especially when the number of decimal points is limited as they are in some computer programs. As his link showed
(1+0.06)^5 = about 1 + 5*0.06 = 1.3 as has been shown. This proceduer is a binomial expansion and if you want a closer approximation, use more terms in the expansion as d-glitches link shows.
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Commented:
If the power is very large (and 5 is not), then there is a faster way to compute the result rather than multiply the base N times. I'll illustrate the idea for N=5:

(1.06)^2 = 1.1236

1.1236^2 = 1.26247696

1.26247696 * 1.06 = 1.3382255776

So the above took 3 multiplies instead of 4. For higher powers, the savings is much more significant.

This works because:

(1.06)^5 = (1.06)^4 * (1.06) = (1.06)^2 * (1.06)^2 * (1.06)

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Author Commented:
Thanks folks I have a question

why do you think it is that when I enter (1.1)exp(5) in excel i get 163.2545
I enter 1.1*1.1*1.1*1.1*1.1 into a calculator and I get the correct answer of 1.611?
Is this a rounding issue?
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Commented:
I think it is a programing error
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Commented:
Please differentiate power (^) with EXP.
If you want to multiple 1.1 five times, you must type =1.1^5 in Excel, so you'll get 1.61051

EXP in Excel is (as copied from Excel 2003 Help):
EXP
Returns e raised to the power of number. The constant e equals 2.71828182845904, the base of the natural logarithm.

Syntax
EXP(number)
Number    is the exponent applied to the base e.

Remarks
To calculate powers of other bases, use the exponentiation operator (^).
EXP is the inverse of LN, the natural logarithm of number.

So =1.1exp(5) is not =1.1^5
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Author Commented:
Thanks Santoso-g!!
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Commented:
In excel, if you enter the following in a cell:
=POWER(1.06,5)
the result is:  1.338225578
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Author Commented:
Hi folks, thanks for your help. One more thing:

fva35=annual deposit * (FVIFA9%35)

fva35=2100.00 * (215.705)

Note that the '35' after fva is in little numbers to the right and slightly below fva.
The 9% and 35 by FVIFA is the same way.

How was 215.705 obtained?

Thanks
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Author Commented:
Hi folks, thanks for your help. One more thing:

fva35=annual deposit * (FVIFA9%35)

fva35=2100.00 * (215.705)

Note that the '35' after fva is in little numbers to the right and slightly below fva.
The 9% and 35 by FVIFA is the same way.

How was 215.705 obtained?

Thanks
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Commented:
"How was 215.705 obtained?"
It is hard to tell. You have not said what the FVIFAS (with the 35 is
Did the 35 appear after the FVIF or after FVIF9%?
-
I suspect that the 35 is just an subscript index selecting a specific FVIF and fva.
My guess is the 9% of FVIF35 = 215.706
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