If $8,500 is invested at 6% compounded continuously, how long will it take to double the investment?
How long will it take the original investment to grow to $14,586.06
See:
http://www.jiskha.com/display.cgi?id=1291958580
To find out how long it will take to double the investment, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount (double the original investment amount)
P = the principal amount (the original investment amount)
r = the interest rate (in decimal form)
t = the time period in years
For this question, we have:
A = $8,500 * 2 = $17,000
P = $8,500
r = 6% = 0.06
Substituting these values into the formula:
$17,000 = $8,500 * e^(0.06t)
To solve for t, we need to isolate the exponential term:
e^(0.06t) = $17,000 / $8,500
e^(0.06t) = 2
Now, take the natural logarithm of both sides to remove the exponential term:
ln(e^(0.06t)) = ln(2)
0.06t = ln(2)
Finally, we can solve for t by dividing both sides by 0.06:
t = ln(2) / 0.06
Using a calculator to evaluate this expression, we find:
t ≈ 11.55 years
Therefore, it will take approximately 11.55 years to double the investment.
Now, let's find out how long it will take for the original investment to grow to $14,586.06.
Using the same formula:
A = $14,586.06
P = $8,500
r = 6% = 0.06
Substituting these values into the formula:
$14,586.06 = $8,500 * e^(0.06t)
Again, isolate the exponential term:
e^(0.06t) = $14,586.06 / $8,500
e^(0.06t) = 1.7160018824
Take the natural logarithm of both sides:
ln(e^(0.06t)) = ln(1.7160018824)
0.06t = ln(1.7160018824)
Divide both sides by 0.06 to solve for t:
t = ln(1.7160018824) / 0.06
Using a calculator, we find:
t ≈ 4.36 years
Therefore, it will take approximately 4.36 years for the original investment to grow to $14,586.06.