1. Understanding r versus (1+r)
Dr. Craig Ruff
Department of Finance
J. Mack Robinson College of Business
Georgia State University
© 2014 Craig Ruff

2. Understanding r versus (1+r)
When one is getting started, multiplying by ‘r’ versus ‘1+r’ is sometimes confusing.
(NOTE: These simple formulas only apply to money invested the whole period.)
Multiplying by (1+r) provides you with your new balance, which contains both principal (the amount you originally invested) plus the interest you earn over the whole period. The ‘1’ picks up the principal and the ‘r’ picks up the interest.
Going back to the $100 invested at 10%, compounded annually. In one year, we would have $100*(1 + .1) distributing the terms…the $100 times the 1 picks up the initial $100 and the $100 times the .1 adds on the interest to give us the balance one year later of $110.
times
times + =
$100*(1 + .1)
$100*(1 + .1)
$110

3. Understanding r versus (1+r)
Just multiplying by r only gives us the interest over the whole period… $100 * .1 = $10.
To sum up (AND ONLY IF INVESTING FOR THE WHOLE YEAR):
$100*(1+.1) = NEW BALANCE (principal plus interest)
$100 * .1 = INTEREST ONLY
Multiplying by r or (1+r) only works if we are investing for the whole period.

4. Understanding r versus (1+r)
Suppose we invest $1,000 at 20%. If we want to know how much money will we have in one year or what is our balance in one year, then we use 1+r:
$1000 * (1.2) = $1,200
Again, the 1 picks up the principal (the $1,000) and the .2 adds on the interest. So, we have principal plus interest.
If we just want to know the interest, then we would just use r as in:
$1,000 * .2 = $200.

5. Understanding r versus (1+r)
This same thinking applies to growth rates, in general.
Suppose sales this year were $100 million. Next year we expect sales to increase 30%.
If we want to know the projected sales for next year, then we use 1+g:
$100,000,000 * (1.3) = $130,000,000.
Again, the 1 picks up the original sales amount (the $100,000,000) and the .3 adds on the 30% growth in sales.
If we just want to know the change in sales, then we would just use g as in:
$100,000,000 * .3 = $30,000,000.

6. Understanding r versus (1+r)
This same thinking holds with a ‘percent-off’ sale.
Suppose a ping pong table normally costs $1000, but it is on sale for 40% off.
If we want to know the sale price, then we use 1+d:
$1,000 * (1-.4) =$1,000 * .6 = $600.
Again, the 1 picks up the original price(the $1,000) and the -.4 subtracts the 40% off of the original price.
If we just want to know how much money we saved, then we would just use d as in:
$1,000 * -.4 = -$400.
I know the ‘+’ looks odd; however, as the discount is a negative number, we are really subtracting the discount.

7. Understanding r versus (1+r)
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