Principal amount (P) = $3100
Final amount (A) = $8200
Interest rate (r) = 3.6% = 0.036
Interest is compounded monthly. So n = 12
Now we can apply compound interest formula as
[tex]A = P(1+ \frac{r}{n})^{nt} [/tex]
Where t is time
Now we can place the value of A , P , r and n
[tex]8200 = 3100(1+ \frac{0.036}{12})^{12*t} [/tex]
Now we can simplify it as
[tex] \frac{8200}{3100} = (1+0.003)^{12t} [/tex]
[tex]2.6452 = (1.003)^{12t}[/tex]
On taking logarithmic function(ln) on both sides
[tex]ln(2.6452) = ln(1.003)^{12t}[/tex]
Now we can use basic property of ln function as [tex]ln(x^a) = aln(x)[/tex]
So we can above expression as
[tex]ln(2.6452) = 12t * ln(1.003)[/tex]
[tex] \frac{ln(2.6452)}{ln(1.003)} = 12t [/tex]
[tex]324.735 = 12t[/tex]
So [tex]t = \frac{324.75}{12} = 27.06 [/tex]
