Answer:
TRUST ME I KNOW!!!!
Explanation:
To determine how long it would take for $10,000 to double at a rate of 5.9%, we can use the concept of compound interest.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (the initial investment)
r is the annual interest rate (expressed as a decimal)
n is the number of times that interest is compounded per year
t is the number of years
In this case, we want to find the time it takes for the principal amount to double, so we can set A = 2P.
2P = P(1 + r/n)^(nt)
Dividing both sides by P:
2 = (1 + r/n)^(nt)
To isolate t, we can take the logarithm of both sides:
log(2) = log[(1 + r/n)^(nt)]
Using logarithmic properties, we can rewrite the equation as:
t = (log(2))/(n * log(1 + r/n))
Given a rate of 5.9% (0.059 as a decimal), we can substitute the values into the formula:
t = (log(2))/(n * log(1 + 0.059/n))
Since the compounding frequency is not provided in the question, we'll assume it's compounded annually (n = 1).
t = (log(2))/(1 * log(1 + 0.059/1))
Simplifying the equation:
t = (log(2))/(log(1.059))
Using a calculator, we can evaluate the expression:
t ≈ (0.693)/(0.056611)
t ≈ 12.22
Rounding to the nearest whole year, it would take approximately 12 years for $10,000 to double at a rate of 5.9%.