Answer:
12.1 years
Step-by-step explanation:
We are given that
Principal amount, P=$3000
Rate of interest, r=6.75% semi-annually
Amount, A=$6700
We know that
When r pays semi-annually
[tex]A=P(1+\frac{r}{n\times 100})^{nt}[/tex]
Where n=2
Using the formula
[tex]6700=3000(1+\frac{6.75}{200})^{2t}[/tex]
[tex]\frac{6700}{3000}=(1..03375)^{2t}[/tex]
[tex]2.233=(1.03375)^{2t}[/tex]
Taking ln on both sides we get
[tex]ln(2.233)=2t ln(1.03375)[/tex]
[tex]2t=\frac{ln(2.233)}{ln(1.03375)}[/tex]
[tex]t=\frac{1}{2}\times \frac{ln(2.233)}{ln(1.03375)}[/tex]
[tex]t=12.1 years[/tex]
