$5,000.00 invested for a period of 6 years doubles to $10,000.00.
What is the interest rate?
You will need to apply logarithms:
<span>log(1 + rate) = {log(total) - log(Principal)} ÷ Years
</span>log(1 + rate) = <span>{log(10,000) - log(5,000)} ÷ 6
</span>log(1 + rate) = (4 - 3.6989700043) / 6
log(1 + rate) =
<span>
<span>
<span>
0.301029957 / 6
</span></span></span>log(1 + rate) =
<span>
<span>
<span>
0.0501716595
</span>
</span>
</span>
Next, raise 10 to the power of
<span>
<span>
<span>
0.0501716595
</span>
</span>
</span>
which results in
<span>
<span>
<span>
1.1224620317
</span>
</span>
</span>
This value represents 1 plus the interest rate, so the interest rate is
0.1224620317 or 12.24620317 percent.
This concludes Part ONE.
Now, onto Part TWO.
How many years does it take for $300 to increase to $9,600 at an annual rate of <span>12.24620317%?
You will use the following formula:
</span>(More logarithms involved).
Years = {log(total) - log(Principal)} ÷ log(1 + rate)
Years = {log(9,600) - log(300)} / log(<span>1.1224620317)
</span>Years = (3.982271233 - 2.4771212547) / 0.050171659518
<span><span><span>Years = 1.5051499783 /
</span>
</span>
</span>.050171659518
Years = 30
There are seven rainbow colors: red, orange, yellow, green, blue, indigo, and violet, so 7 possible choices. When two events occur in sequence, multiply their probabilities. With replacement: P(violet)=1/7 and P(orange)=1/7, so P(violet then orange)=1/7 * 1/7 = 1/49. Without replacement: after picking violet, P(orange)=1/6, so P(violet then orange)=1/7 * 1/6 = 1/42.
