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