How long does it take an investment to quadruple in value if the investment yields 6% per year?

Explanation:

If the investment yield 6% per year, each year its value is multiplied by 1.06.

After 2 years, the value is multiplied by 1.06², after 3 years it is multiplied by 1.06³, and so on.

After n years, the value is multiplied by 1.06ⁿ.

You want that the investment quadruples, thus the multiplicative factor is 4, meaning that you want to solve for:

If you do not know logarithms, you can solve by succesive iterations:

Thus, if an investement yields 6% per years, it takes 24 years the investment to quadruple in value.

If you know logarithms, you can make n the subject of the equation:

Again, the solution is 24 years.

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