Given that,
Principal amount, P = 2000 dollars
Rate of interest, r = 6.75% = 0.0675
Final amount, A = 2900 dollars
The formula to find the final amount in a compound interest is,
A = P (1 +
)^ (nt)
n = number of times interest compounded in a year = 12 (Since compounded monthly.
Substituting the given values,
![2900 = 2000 \huge \text[1 + \huge \text((0.0675)/(12) \huge \text)\huge \text]^((12t))](https://img.qammunity.org/2024/formulas/mathematics/high-school/xw3y48htsc8c9aaczghgpuif7rhewejm6u.png)



Taking logarithms on both sides,


Hence the time that the person must keep the money is 5.5 years.