Consider a $100 investment earning 12% compounded quarterly. How long will it take to triple your money? Round your answer to the nearest tenth of a year.

(1+.12/4)^(4x) = 3

x = 9.3 years

Makes sense. The Rule of 72 says it will double in about 6 years.

To answer this question, we need to use the compound interest formula:

A = P * (1 + r/n)^(nt)

Where:
A is the final amount after time t
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the time in years

In this case, the principal amount is $100, the annual interest rate is 12%, compounded quarterly (n = 4), and we want to find the time it takes for the investment to triple (A = 3P).

Let's solve the equation for t:

3P = P * (1 + r/n)^(nt)

Divide both sides of the equation by P:

3 = (1 + r/n)^(nt)

Take the natural logarithm of both sides to isolate nt:

ln(3) = nt * ln(1 + r/n)

We can now solve for t. Rearrange the equation:

t = ln(3) / (n * ln(1 + r/n))

Substituting the given values:

t = ln(3) / (4 * ln(1 + 0.12/4))

Calculating:

t ≈ ln(3) / (4 * ln(1.03))

t ≈ ln(3) / (4 * 0.0307)

t ≈ ln(3) / 0.1229

t ≈ 5.66 (rounded to two decimal places)

Therefore, it will take approximately 5.7 years (rounded to the nearest tenth of a year) to triple your money with a 12% annual interest rate compounded quarterly.