Data:
P = 5.300,00
A = 7.000,00
r = 9% = 0,09
n = 4
t = ?
We have the following compound interest formula:
[tex]A = P*(1+ \frac{r}{n})^{nt} [/tex]
[tex]7000 = 5300*(1+ \frac{0.09}{4})^{4t} [/tex]
[tex]7000 = 5300*(1+ 0.0225)^{4t}[/tex]
[tex]7000 = 5300*(1.0225)^{4t}[/tex]
[tex](1.0225)^{4t} = \frac{7000}{5300} [/tex]
[tex](1.0225)^{4t} = 1.32075[/tex]
Now, take the natural logarithm of both sides:
[tex]ln(1.0225^{4t}) = ln(1.32075)[/tex]
[tex]4*t*ln(1.0225) = = ln(1.32075)[/tex]
[tex]4*t = \frac{ln(1.32075)}{ln(1.0225)} [/tex]
[tex]4t = 12.50301769...[/tex]
[tex]4t \approx 12.50302[/tex]
[tex]t \approx \frac{12.50302}{4} [/tex]
[tex]\boxed{t \approx 3.1258years}[/tex]
Therefore, we have: (answer)
3 years 1 month and 16 days
