Question

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

Answer 1

Answer:

• 24 years

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:

• 1.06ⁿ = 4

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

• 1.06² = 1.1236
• 1.06⁴ = 1.2625
• 1.06¹⁰ = 1.79
• 1.06²⁰ = 3.2
• 1.06³⁰ = 5.7
• 1.06²⁵ = 4.29
• 1.06²⁴ = 4.05
• 1.06²³ = 3.82

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:

       $1.06^n=4\\\\n\log 1.06=\log 4\\\\n=\dfrac{\log 4}{\log 1.06}=23.79\approx 24$

Again, the solution is 24 years.