Question

Im doing my math homework and this question came up, and i dont know what to do. Can someone please help?

Answer 1

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