Answer :
the compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where A is the amount you will have, P is the principal, r is the annual interest rate, n is the amount of times the interest is compounded per time period, and t is the amount of time.
In our case, we need to find the time t. Then, by moving the Principal to the left hand side, we get
[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]By applying natural logarithm on both sides, we get
[tex]\ln (\frac{A}{P})=nt\cdot ln(1+\frac{r}{n})[/tex]now, we can isolate t as
[tex]t=\frac{\ln (\frac{A}{P})}{n\ln (1+\frac{r}{n})}[/tex]Now, we can substitute our given values into this expression. It yields,
[tex]t=\frac{\ln (\frac{6550}{6000})}{12\ln (1+\frac{0.1}{12})}[/tex]which gives
[tex]t=\frac{0.0877}{12(0.0083)}[/tex]then, the time (in years) is
[tex]t=0.88\text{ years}[/tex]Now, we must convert this result in months. Since 1 year has 12 months, we have
[tex]\begin{gathered} t=0.88\times12 \\ t=10.56\text{ months} \end{gathered}[/tex]that is, the answer is 10.56 months