The Compound Interest Equation
P = C (1 + r/n) ntwhere
P = future value
C = initial deposit
r = interest rate (expressed as a fraction: eg. 0.06)
n = # of times per year interest is compounded
t = number of years invested
Simplified Compound Interest Equation
When interest is only compounded once per year (n=1), the equation simplifies to:P = C (1 + r) t
Continuous Compound Interest
When interest is compounded continually (i.e. n -->
), the compound interest equation takes the form:P = C e rt
Demonstration of Various Compounding
The following table shows the final principal (P), after t = 1 year, of an account initially with C = $10000, at 6% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect.| n | P |
| 1 (yearly) | $ 10600.00 |
| 2 (semiannually) | $ 10609.00 |
| 4 (quarterly) | $ 10613.64 |
| 12 (monthly) | $ 10616.78 |
| 52 (weekly) | $ 10618.00 |
| 365 (daily) | $ 10618.31 |
| continuous | $ 10618.37 |
Loan Balance
Situation: A person initially borrows an amount A and in return agrees to make n repayments per year, each of an amount P. While the person is repaying the loan, interest is accumulating at an annual percentage rate of r, and this interest is compounded n times a year (along with each payment). Therefore, the person must continue paying these installments of amount P until the original amount and any accumulated interest is repaid. This equation gives the amount B that the person still needs to repay after t years.where
B = A (1 + r/n)NT - P (1 + r/n)NT - 1
(1 + r/n) - 1
B = balance after t years
A = amount borrowed
n = number of payments per year
P = amount paid per payment
r = annual percentage rate (APR
Unit Conversion Tables for Volumes
A note on the metric system:Before you use this table, convert to the base measurement first. For example, convert centimeters to meters, kilograms to grams, etc.The notation 1.23E - 4 stands for 1.23 x 10-4 = 0.000123.
| from \ to | = __ feet3 | = __ gallons | = __ inches3 | = __ liters | = __ meters3 | = __ miles3 | = __ pints | = __ quarts | = __ yards3 |
| foot3 | 7.480519... | 1728 | 28.31684... | 0.02831684... | 59.84415... | 29.92207... | (1/27) | ||
| gallon | 0.1336805... | 231 | 3.785411... | 0.003785411... | 8 | 4 | 0.004951131... | ||
| inch3 | (1/1728) | (1/231) | 0.01638706... | 1.638706...E - 5 | (1/28.875) | (1/57.75) | (1/46656) | ||
| liter | 0.03531466... | 0.2641720... | 61.02374... | (1/1000) | 2.113376... | 1.056688... | 0.001307950... | ||
| meter3 | 35.31466... | 264.1720... | 61023.74... | 1000 | 2113.376... | 1056.688... | 1.307950... | ||
| mile3 | |||||||||
| pint | 0.01671006... | (1/8) | 28.875 | 0.4731764... | (1/2) | ||||
| quart | 0.03342013... | (1/4) | 57.75 | 0.94635... | 2 | 0.001237782... | |||
| yard3 | 27 | 201.974... | 46656 | 764.555... | 0.7645548... | 1615.792... | 807.8961... |
Examples: foot3 = 1728 inches3; 2 feet3 = 2x1728 inches2.
Useful Exact Volume Relationships
fluid ounce = (1/8) cup = (1/16) pint = (1/32) quart = (1/128) gallonUseful Exact Length Relationships
gallon = 128 fluid ounces = 231 inches3 = 8 pints = 4 quarts
quart = 32 fluid ounces = 4 cups = 2 pints = (1/4) gallon
cup = 8 fluid ounces = (1/2) pint = (1/4) quart = (1/16) gallonNote that when converting volume units:
mile = 63360 inches = 5280 feet = 1760 yards
yard = 36 inches = 3 feet = (1/1760) mile
foot = 12 inches = (1/3) yard = (1/5280) mile
pint = 16 fluid ounces = (1/2) quart = (1/8) gallon
inch = 2.54 centimeters = (1/12) foot = (1/36) yard
liter = 1000 centimeters3 = 1 decimeter3 = (1/1000) meter3
1 foot = 12 inches
(1 foot)3 = (12 inches)3 (cube both sides)
1 foot3 = 1728 inches3
The linear & volume relationships are not the same!
Unit Conversion Tables for Areas
A note on the metric system:Before you use this table convert to the base measurement first. For example, convert centimeters to meters, convert kilograms to grams.The notation 1.23E - 4 stands for 1.23 x 10-4 = 0.000123.
| from \ to | = __ acres | = __ feet2 | = __ inches2 | = __ meters2 | = __ miles2 | = __ yards2 |
| acre | 43560 | 6272640 | 4046.856... | (1/640) | 4840 | |
| foot2 | (1/43560) | 144 | 0.09290304 | (1/27878400) | (1/9) | |
| inch2 | (1/6272640) | (1/144) | (1/1296) | |||
| meter2 | 1550.0031 | |||||
| mile2 | 640 | 27878400 | 3097600 | |||
| yard2 | (1/4840) | 9 | 1296 | 0.83612736 |
Examples: foot2 = 144 inches2; 2 feet2 = 2x144 inches2.
Useful Exact Area & Length Relationships
acre = (1/640) miles2Note that when converting area units:
mile = 1760 yards = 5280 feet
yard = 3 feet = 36 inches
foot = 12 inches
inch = 2.54 centimeters
1 foot = 12 inches
(1 foot)2 = (12 inches)2 (square both sides)
1 foot2 = 144 inches2
The linear & area relationships are not the same!
Unit Conversion Tables for Lengths & Distances
A note on the metric system:Before you use this table, convert to the base measurement first. For example, convert centimeters to meters, convert kilograms to grams.The notation 1.23E - 4 stands for 1.23 x 10-4 = 0.000123.
| from \ to | = __ feet | = __ inches | = __ meters | = __ miles | = __ yards |
| foot | 12 | 0.3048 | (1/5280) | (1/3) | |
| inch | (1/12) | 0.0254 | (1/63360) | (1/36) | |
| meter | 3.280839... | 39.37007... | 1.093613... | ||
| mile | 5280 | 63360 | 1609.344 | 1760 | |
| yard | 3 | 36 | 0.9144 | (1/1760) |
Examples: foot = 12 inches; 2 feet = 2x12 inches.
Useful Exact Length Relationships
mile = 1760 yards = 5280 feet
yard = 3 feet = 36 inches
foot = 12 inches
inch = 2.54 centimeters
Fraction to Decimal Conversion Tables
Important Note: any span of numbers that is underlined signifies that those numbers are repeated. For example, 0.09 signifies 0.090909....
Only fractions in lowest terms are listed. For instance, to find 2/8, first simplify it to 1/4 then search for it in the table below.
| fraction = decimal | |||
| 1/1 = 1 | |||
| 1/2 = 0.5 | |||
| 1/3 = 0.3 | 2/3 = 0.6 | ||
| 1/4 = 0.25 | 3/4 = 0.75 | ||
| 1/5 = 0.2 | 2/5 = 0.4 | 3/5 = 0.6 | 4/5 = 0.8 |
| 1/6 = 0.16 | 5/6 = 0.83 | ||
| 1/7 = 0.142857 | 2/7 = 0.285714 | 3/7 = 0.428571 | 4/7 = 0.571428 |
| 5/7 = 0.714285 | 6/7 = 0.857142 | ||
| 1/8 = 0.125 | 3/8 = 0.375 | 5/8 = 0.625 | 7/8 = 0.875 |
| 1/9 = 0.1 | 2/9 = 0.2 | 4/9 = 0.4 | 5/9 = 0.5 |
| 7/9 = 0.7 | 8/9 = 0.8 | ||
| 1/10 = 0.1 | 3/10 = 0.3 | 7/10 = 0.7 | 9/10 = 0.9 |
| 1/11 = 0.09 | 2/11 = 0.18 | 3/11 = 0.27 | 4/11 = 0.36 |
| 5/11 = 0.45 | 6/11 = 0.54 | 7/11 = 0.63 | |
| 8/11 = 0.72 | 9/11 = 0.81 | 10/11 = 0.90 | |
| 1/12 = 0.083 | 5/12 = 0.416 | 7/12 = 0.583 | 11/12 = 0.916 |
| 1/16 = 0.0625 | 3/16 = 0.1875 | 5/16 = 0.3125 | 7/16 = 0.4375 |
| 11/16 = 0.6875 | 13/16 = 0.8125 | 15/16 = 0.9375 | |
| 1/32 = 0.03125 | 3/32 = 0.09375 | 5/32 = 0.15625 | 7/32 = 0.21875 |
| 9/32 = 0.28125 | 11/32 = 0.34375 | 13/32 = 0.40625 | |
| 15/32 = 0.46875 | 17/32 = 0.53125 | 19/32 = 0.59375 | |
| 21/32 = 0.65625 | 23/32 = 0.71875 | 25/32 = 0.78125 | |
| 27/32 = 0.84375 | 29/32 = 0.90625 | 31/32 = 0.96875 |
Need to convert a repeating decimal to a fraction? Follow these examples:
Note the following pattern for repeating decimals:
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999
Division by 9's causes the repeating pattern.
Note the following pattern for repeating decimals:
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999
Division by 9's causes the repeating pattern.
Note the pattern if zeros precede the repeating decimal:
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900
Adding zero's to the denominator adds zero's before the repeating decimal.
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900
Adding zero's to the denominator adds zero's before the repeating decimal.
To convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating part and the repeating part.
0.21 + 0.00456456456456456...
Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.
21/100 + 456/99900
Now add these fraction by expressing both with a common divisor
20979/99900 + 456/99900
and add.
21435/99900
Finally simplify it to lowest terms
1429/6660
and check on your calculator or with long division.
= 0.2145645645...
0.21 + 0.00456456456456456...
Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.
21/100 + 456/99900
Now add these fraction by expressing both with a common divisor
20979/99900 + 456/99900
and add.
21435/99900
Finally simplify it to lowest terms
1429/6660
and check on your calculator or with long division.
= 0.2145645645...
I am not a very well read Individual,However you are doing a good and omen job I can say.The basic norm we read in chemistry was that when one element donates(gives out some thing willingly) a particle (electron),it gains a +ve charge on it and that is what you are doing .Keep it on....all the best.
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