Answer:
3.63 years
Step-by-step explanation:
The formula would be of compound growth, which is:
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]
Where
F is future amount (with interest)
P is initial deposit
r is rate of interest in a year
n is number of compounding in 1 year
t is the time in years
Given in this problem:
To accumulate 2000 interest means the future amount will be:
10000+2000 = 12,000
Present amount is 10,000
r is the annual interest, which is 5% or 0.05
compounded monthly means, 12 times a year, so n = 12
t is time in years, which we need to find
Substituting, we have:
[tex]F=P(1+\frac{r}{n})^{nt}\\12000=10000(1+\frac{0.05}{12})^{12t}\\1.2=(1.0042)^{12t}\\Ln(1.2)=Ln((1.0042)^{12t})\\Ln(1.2)=12t*Ln(1.0042)\\12t=\frac{Ln(1.2)}{Ln(1.0042)}\\12t=43.50099\\t=3.63[/tex]
The time it will take is around 3.63 years
