Christina has $15000$ euro and wants to buy a car. Presently, this car costs $24800$ euro. Christina will put the $15000$ euro in the bank with a monthly interest rate of $.6\%$. The car devaluates $.8\%$ a month.
How many months will it take until Christina is able to buy the car?
I did:
$$15000 \cdot (1+.6)^t = 24800 \cdot (1-.8)^t \Leftrightarrow \frac{15000}{24800} = \frac{.2^t}{1.6^t} \Leftrightarrow \frac{75}{124} = (\frac{.2}{1.6})^t \Leftrightarrow \frac{75}{124} = (\frac{5}{40})^t \Leftrightarrow \frac{75}{124} = (\frac{1}{8})^t \Leftrightarrow \log_{\frac{1}{8}}(\frac{75}{124})=t \Leftrightarrow t \approx .24179...$$
But this result doesn't make any sense. My book says the solution is 36 months.
What did I do wrong?
$.6\%$ is $.006$. Do likewise for $.8\%$. Your error comes from using $.6\%$ as $.6$, which equals $60\%$.