Final answer:
To calculate the number of years it would take for your account to reach $3,105.85, you can use the formula for compound interest: A = P(1 + r/n)^(nt). In this case, it takes approximately 9.25 years for the account to reach $3,105.85.
Step-by-step explanation:
To calculate the number of years it would take for your account to reach $3,105.85, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the principal amount (initial investment)
r is the annual interest rate (as a decimal)
n is the number of times interest is compounded per year
t is the number of years
In this case, the principal amount is $1,000, the annual interest rate is 12% (0.12 as a decimal), and the final amount is $3,105.85. Let's calculate the number of years:
$3,105.85 = $1,000(1 + 0.12/n)^(n*t)
By trial and error, we can find that it takes approximately 9.25 years for the account to reach $3,105.85.