Answer: To find out how long it will take for the balance to triple, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
Where:
A is the final amount,
P is the initial deposit (600),
r is the annual interest rate (6%),
n is the number of times the interest is compounded per year (12 times per year, or monthly),
t is the time in years.
To find t, we'll set A equal to 3 * P and solve for t:
3 * P = P * (1 + r/n)^(nt)
Expanding the right-hand side:
3 * P = P * (1 + 0.06/12)^(12t)
Dividing both sides by P:
3 = (1 + 0.06/12)^(12t)
Taking the natural logarithm of both sides:
ln 3 = ln((1 + 0.06/12)^(12t))
Using the logarithmic rule for exponentiation:
ln 3 = (12t) * ln(1 + 0.06/12)
Dividing both sides by ln(1 + 0.06/12):
ln 3 / ln(1 + 0.06/12) = 12t
Using a logarithm calculator, we find that ln 3 / ln(1 + 0.06/12) = 15.57.
Finally, dividing by 12 to find t in years:
t = 15.57 / 12 = 1.298 years, or approximately 1 year and 4 months.
So, it will take approximately 1 year and 4 months for the balance to triple.