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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?

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  • 1
    $\begingroup$ The $.6$ and $.8$ should be $0.006$ and $0.008$ because they are percentages. $\endgroup$ – AndroidFish Nov 25 '16 at 3:42
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$.6\%$ is $.006$. Do likewise for $.8\%$. Your error comes from using $.6\%$ as $.6$, which equals $60\%$.

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