Perry has an opportunity to put $12,000 into an investment with an APR of 5.6% compounded annually.
How long will it take his investment to double?
(round to one decimal place)
24000=12000(1+.056)^n
2=(1.056)^n
take log of each side.
log2=n log(1.056)
n=log2/log(1.056)
put this in your google search window: log(2)/log(1.056)=12.72
so n= 13 years.
To determine how long it will take for Perry's investment to double, we need to use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (in this case, it will be double the initial investment, which is $12,000 * 2 = $24,000)
P = the principal amount (in this case, $12,000)
r = the annual interest rate expressed as a decimal (in this case, 5.6% = 0.056)
n = the number of times interest is compounded per year (since it is compounded annually, n = 1)
t = the time in years
Substituting the values into the formula, we have:
$24,000 = $12,000(1 + 0.056/1)^(1*t)
Next, we can divide both sides of the equation by $12,000 to simplify:
2 = (1 + 0.056)^(t)
Since we want to solve for t, we can take the logarithm of both sides using a logarithm base that cancels out the exponent on the right side. In this case, we can use the natural logarithm (ln):
ln(2) = ln((1 + 0.056)^(t))
Using the properties of logarithms, we can bring the exponent down and solve for t:
ln(2) = t * ln(1 + 0.056)
Dividing both sides of the equation by ln(1 + 0.056), we can isolate t:
t = ln(2) / ln(1 + 0.056)
Calculating the values on the right side, we find:
t ≈ 12.50
Therefore, it will take Perry's investment approximately 12.5 years to double. (Rounded to one decimal place)