If you are considering a long-term investment that earns a rate of 10% APR, how long will it take for your investment to quadruple?

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Assuming the interest was compounded once a year, one is income would be defined by the function:

N = P(1.10)^t

Where N = The total value of ur investment
Where P = The initial amount invested
Where t = The amount of time that the money was invested.

In the given scenario, u want ur initial amount invested to quadruple, so u want:

N = 4P

Substituting this into the first equation gives you:

4P = P(1.10)^t

Divide both sides by P:

4 = (1.10)^t

Taking the log of both sides:

log[4] = log[(1.10)^t]

Applying the log property log[a^b] = b*log[a]:

log[4] = t*log[1.10]

Solving for t:

t = log[4]/log[1.10]

t = 14.5 years

Thus, it will take about 14.5 years to quadruple an initial investment earning 10% APR.

As a side note, if the interested was compounded continuously (i.e. not once a year, but rather every moment for an entire year), it would take about 13.9 years to quadruple the investment. For most (non-bank) investments, u r effectively compounding ur money once a year, not continuously.

Rule of 72: Divide 72 by the interest rate to determine how long it will take to double.

72 divided by 10 = 7.2 years to double. To quadruple? Just double that. roughly 14.4 years.

l hope that is a math problem, because if you were faced with a real investment earning 10% right now you're taking a lot of risk!