Using the rule that states that log a = log b is equivalent to a = b, we can write:
1.102814 = 1.004458333312t
To solve for t, we can isolate it by dividing both sides of the equation by 1.004458333312:
1.102814/1.004458333312 = t
t ≈ 1.096 years
Since the annual interest is compounded monthly, we need to multiply t by 12 to get the number of months:
t(months) ≈ 13.15 months
Rounding to the nearest month, we get:
t(months) ≈ 13 months
Therefore, it takes approximately 13 months for a $10,000 investment to grow to $11,028.14 in a savings account where the annual interest is compounded monthly. Answer: 1 months.