Final answer:
To find the future value of an account with compound interest, use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the annual interest rate, n is the compounding frequency, and t is the time period. Plugging in the given values, the future value is approximately $10,978.15.
Step-by-step explanation:
To find the future value of an account, given the principal amount, interest rate, compounding frequency, and time period, we can use the formula for compound interest. The formula for compound interest is:
A = P(1 + r/n)^(nt)
where A is the future value, P is the principal amount, r is the annual 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 $7,800, the interest rate is 5.5% (or 0.055 as a decimal), the compounding frequency is weekly (which means n = 52), and the time period is 7 years.
Plugging these values into the formula, we get:
A = 7800(1 + 0.055/52)^(52*7) = $10,978.15
Therefore, the future value of the account after 7 years would be approximately $10,978.15.