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Yuri
21 day ago
10

Five thousand dollars compounded annually at an x% interest rate takes six years to double. At the same interest rate, how many

years will it take $300 to grow to $9600?
Mathematics
1 answer:
Leona [9.2K]21 day ago
3 0
$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


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The area of the shaded part is 42.50 cm².

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Examine the diagram provided.

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