Final answer:
To find the final amount of money in an account with compound interest, we use the formula A = P(1 + r/n)^(nt). Plugging in the given values, the final amount is approximately $11,877.62.
Step-by-step explanation:
To find the final amount of money in an account with compound interest, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount of money
- P is the principal amount (initial deposit)
- r is the annual interest rate (as a decimal)
- n is the number of times the interest is compounded per year
- t is the number of years the money is left in the account
In this case, the principal amount (P) is $7,700, the annual interest rate (r) is 7%, the interest is compounded semiannually (n = 2), and the money is left for 8 years (t = 8).
Plugging these values into the formula:
A = 7700(1 + 0.07/2)^(2*8)
Calculating this expression:
A ≈ $11,877.62
So, the final amount of money in the account after 8 years will be approximately $11,877.62.