Final answer:
The initial deposit of $800 earning 8% interest compounded monthly over 5 1/2 years is calculated using the formula for future value of a compounded investment. The answer can be found via the formula FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Step-by-step explanation:
The question involves calculating the future value of an investment with compound interest. Given that the initial deposit is $800 and the interest rate is 8% compounded monthly, the formula for the future value (FV) of a compounded investment is FV = P(1 + r/n)nt. Here, P is the principal amount ($800), r is the annual interest rate (0.08), n is the number of times the interest is compounded per year (12, because it's compounded monthly), and t is the time in years (5.5).
Plugging in these numbers, we get:
FV = 800(1 + 0.08/12)12*(5.5)
Now, calculate the value inside the parentheses and raise it to the power:
FV = 800(1 + 0.00666667)66
The next step would be to use a calculator to compute the exact amount. The final amount will be the value of the account after 5 1/2 years.