Final answer:
To reach $3,000 in an account that pays 3.5% interest compounded monthly with $50 monthly deposits, it is not possible.
Step-by-step explanation:
To find out how long it will take to have $3,000 in the account, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded in a year, and t is the number of years.
In this case, the principal is $0 (since you start with no money), the interest rate is 3.5% (as a decimal, 0.035), the interest is compounded monthly (so n = 12), and we want to find t when A = $3,000.
Substituting the values, we have:
$3,000 = 0(1 + 0.035/12)^(12t)
Since we can't raise zero to any power to get a non-zero value, we can conclude that it is not possible to reach $3,000 in this account with only $50 monthly deposits.
Therefore, none of the given options (a, b, c, or d) are correct.