how long does it take $450 to double at simple interest rate of 14%

450(1.14)^n = 900

1.14^n = 2
take log of both sides

log 1.14^n = log 2
n log1.14 = log2
n = log2/log1.14 = appr 5.3 years

How long does it take $450 to double at a simple interest rate of 14%

To calculate the time it takes for an amount to double at a simple interest rate, we can use the formula:

Time (in years) = (A / P) / (r * 100)

Where:
A = Final amount
P = Principal amount (initial amount)
r = Interest rate (in decimal form)

In this case:
A = 2 * $450 = $900
P = $450
r = 14% = 14/100 = 0.14

Let's substitute these values into the formula:

Time (in years) = ($900 / $450) / (0.14 * 100)

Time (in years) = 2 / (0.14 * 100)

Time (in years) = 2 / 0.014

Time (in years) ≈ 142.857

Therefore, it would take approximately 142.857 years for $450 to double at a simple interest rate of 14%.

To calculate the amount of time it takes for an investment to double at a simple interest rate, we can use the formula:

\(\displaystyle t=\frac{{\ln \left( \frac{{A}}{{P}} \right)}}{{r}}\)

where:
\(t\) is the time in years,
\(A\) is the final amount,
\(P\) is the initial principal, and
\(r\) is the interest rate.

In this case, the principal (\(P\)) is $450, and the interest rate (\(r\)) is 14%.

To find the final amount (\(A\)), we can use the formula:

\(\displaystyle A=P\left( 1 + \frac{{rt}}{{100}} \right)\)

where \(t\) is the time in years.

Let's substitute the known values into the formula:

\(\displaystyle A=450 \left( 1 + \frac{{14t}}{{100}} \right)\)

To double the initial amount, the final amount (\(A\)) should be $900. Therefore:

\(\displaystyle 900=450 \left( 1 + \frac{{14t}}{{100}} \right)\)

Now, let's solve for \(t\).

\(\displaystyle \frac{{900}}{{450}}= 1 + \frac{{14t}}{{100}}\)

\(\displaystyle 2=1 + \frac{{14t}}{{100}}\)

Subtracting 1 from both sides:

\(\displaystyle 1= \frac{{14t}}{{100}}\)

To isolate \(t\), we can multiply both sides by \(\displaystyle \frac{{100}}{{14}}\):

\(\displaystyle \frac{{100}}{{14}}=\frac{{14t}}{{100}}\)

\(\displaystyle 7\frac{{1}}{{14}}=t\)

So, it would take approximately 7.07 years for $450 to double at a simple interest rate of 14%.