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+ (r)/(n))^(nt)`

`7000 = 5300*(1+ (0.09)/(4))^(4t)`

`7000 = 5300*(1+ 0.0225)^(4t)`

`7000 = 5300*(1.0225)^(4t)`

`(1.0225)^(4t) = (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 = (ln(1.32075))/(ln(1.0225))`

`4t = 12.50301769...`

`4t \approx 12.50302`

`t \approx (12.50302)/(4)`

`\boxed{t \approx 3.1258years}`

Therefore, we have: (answer)

3 years 1 month and 16 days