Answer:
- <u>24 years</u>
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Explanation:
If<em> the investment yield 6% per year</em>, 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 <em>the investment quadruples</em>, 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, <em>if an investement yields 6% per years</em>, it takes 24 years t<em>he investment to quadruple in value.</em>
If you know logarithms, you can make n the subject of the equation:
Again, the solution is 24 years.