The formula, it would take approximately 8.30 years for the investment to reach $30,000.
The formula to calculate the value of the investment over time, given a yearly growth rate of 5%, would be:
V(t) be the value of the investment at year t after 2016.
r be the annual rate of increase (5% in this case).
V0 be the initial value of the investment ($20,000).
We know that the investment grows by a factor of 1+r each year. So:
V(t) = V0 * (1 + r)^t
Substituting the given values:
V(t) = 20000 * (1 + 0.05)^t
Value in 2028:
2028 is 12 years after 2016, so:
V(12) = 20000 * (1 + 0.05)^12
V(12) = 20000 * (1.05)^12
V(12) = 20000 * 1.795856
≈ $35917.12
To solve for the time it takes to reach $30,000 using the formula
t×ln(1+r)=ln( V(t)/ V_0):
Given V_0 =20000,V(t)=30000,r=0.05
t×ln(1+0.05)=ln( 30000/ 20000)
t×ln(1.05)=ln(1.5)
Now, solve for t:
t= ln(1.5)/ ln(1.05)
t≈ 0.4055/ 0.0488
t≈8.30
Therefore, according to the formula, it would take approximately 8.30 years for the investment to reach $30,000.