If you 2

If you deposit $4000 into an account paying 9% annual interest compounded monthly, how long until there is $10000 in the account?

Correct answer:

t =  123 m

Step-by-step explanation:

$$\begin{gathered} p=9\mathrm{\%}={\displaystyle \frac{9}{100}}=0.09 \\ i=1+p\mathrm{/}12=1+0.09\mathrm{/}12={\displaystyle \frac{403}{400}}=1.0075 \\ 4000\cdot i^t=10000 \\ {i}^t=10000\mathrm{/}4000 \\ t\log i=\log 10000\mathrm{/}4000 \\ {t}_1={\displaystyle \frac{\log (10000\mathrm{/}4000)}{\log (i)}}={\displaystyle \frac{\log (10000\mathrm{/}4000)}{\log (1.0075)}}\doteq 122.6297\text{ m } \\ t=\lceil t_1\rceil =\lceil 122.6297\rceil =123\text{ m} \end{gathered}$$

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