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Getting rich the slow, boring way

Many U.S. citizens can accumulate a large amount of wealth during their lifetimes, if they make two key choices. The first is to complete additional education and training. In 2014, the U.S. Census Bureau reported median earnings for households where the main earner had only a high school degree of $33,124; for those with a two-year associate degree, median earnings were $40,560 and for those with a four-year bachelor’s degree, median income was $54,340. Learning is not only good for you, but it pays off financially, too.

The second key choice is to start saving money early in life, and to give the power of compound interest a chance. Imagine that at age 25, you save $3,000 and place that money into an account that you do not touch. In the long run, it is not unreasonable to assume a 7% real annual rate of return (that is, 7% above the rate of inflation) on money invested in a well-diversified stock portfolio. After 40 years, using the formula for compound interest, the original $3,000 investment will have multiplied nearly fifteen fold:

3 , 000 ( 1 + .07 ) 40 = $ 44,923

Having $45,000 does not make you a millionaire. Notice, however, that this tidy sum is the result of saving $3,000 exactly once. Saving that amount every year for several decades—or saving more as income rises—will multiply the total considerably. This type of wealth will not rival the riches of Microsoft CEO Bill Gates, but remember that only half of Americans have any money in mutual funds at all. Accumulating hundreds of thousands of dollars by retirement is a perfectly achievable goal for a well-educated person who starts saving early in life—and that amount of accumulated wealth will put you at or near the top 10% of all American households. The following Work It Out feature shows the difference between simple and compound interest, and the power of compound interest.

Simple and compound interest

Simple interest is an interest rate calculation only on the principal amount.

Step 1. Learn the formula for simple interest:

Principal × Rate × Time = Interest

Step 2. Practice using the simple interest formula.

Example 1: $100 Deposit at a simple interest rate of 5% held for one year is:

$100 × 0.05 × 1 = $5

Simple interest in this example is $5.

Example 2: $100 Deposit at a simple interest rate of 5% held for three years is:

$100 × 0.05 × 3 = $15

Simple interest in this example is $5.

Step 3. Calculate the total future amount using this formula:

Total future amount = principal + interest

Step 4. Put the two simple interest formulas together.

Total future amount (with simple interest) = Principal + (Principal × Rate × Time)

Step 5. Apply the simple interest formula to our three year example.

Total future amount (with simple interest) = $100 + ($100 × 0.05 × 3) = $115

Compound interest is an interest rate calculation on the principal plus the accumulated interest.

Step 6. To find the compound interest, we determine the difference between the future value and the present value of the principal. This is accomplished as follows:

Future Value = Principal  ×   ( 1 + interest rate ) time
Compound interest = Future Value – Present Valve

Step 7. Apply this formula to our three-year scenario. Follow the calculations in

[link]

Year 1
Amount in Bank $100
Bank Interest Rate 5%
Total $105
$100 + ($100 × 0.5)
Year 2
Amount in Bank $105
Bank Interest Rate 5%
Total $110.25
$105 + ($105 × .05)
Year 3
Amount in Bank $110.25
Bank Interest Rate 5%
Total $115.75
$110.25 + ($110.25 × .05)
Compound interest $115.75 – $100 = $15.75

Step 8. Note that, after three years, the total is $115.75. Therefore the total compound interest is $15.75. This is $0.75 more than was obtained with simple interest. While this may not seem like much, keep in mind that we were only working with $100 and over a relatively short time period. Compound interest can make a huge difference with larger sums of money and over longer periods of time.

Questions & Answers

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Differences Between Laspeyres and Paasche Indices
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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Source:  OpenStax, Openstax microeconomics in ten weeks. OpenStax CNX. Sep 03, 2014 Download for free at http://legacy.cnx.org/content/col11703/1.2
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