Answer:
It takes 75 years for the investment to quadruple in value
Step-by-step explanation:
Simple Interest
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
In this question:
4% simple interest per year, so I = 0.04.
Quadruple:
t when T = 4P.
The interest earned is:
[tex]T = E + P[/tex]
[tex]4P = E + P[/tex]
[tex]E = 3P[/tex]
Now we find the time.
[tex]E = P*0.04*t[/tex]
[tex]3P = P*0.04*t[/tex]
[tex]0.04t = 3[/tex]
[tex]t = \frac{3}{0.04}[/tex]
[tex]t = 75[/tex]
It takes 75 years for the investment to quadruple in value
