Compound Interest

If you deposit $6000 in an account paying 6.5% annual interest compounded quarterly, how long will it take for the account to have $12600?

Correct answer:

t =  141 m

Step-by-step explanation:

$$\begin{gathered} i=1+6.5/100/4=\frac{813}{800}\doteq 1.0163 \\ 6000\cdot i^n=12600 \\ {i}^n=12600/6000 \\ n\log i=\log 12600/6000 \\ n=\frac{\log (12600/6000)}{\log i}=\frac{\log (12600/6000)}{\log 1.0163}\doteq 46.0277\text{q} \\ {n}_1=\lceil n\rceil =\lceil 46.0277\rceil =47 \\ t=12/4\cdot n_1=12/4\cdot 47=141\text{m} \end{gathered}$$

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