Final answer:
The balance after 8 years with a $400 deposit at a 7% interest rate compounded monthly is $677.62.
Step-by-step explanation:
To find the balance after 8 years, we can use the formula for compound interest: A = P(1+r/n)^(nt), where A is the final balance, P is the principal amount (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, the principal amount is $400, the interest rate is 7%, and interest is compounded monthly. So, the formula becomes A = 400(1+0.07/12)^(12*8).
Simplifying the equation gives A = $677.62. Therefore, the balance after 8 years will be $677.62.