Final answer:
The problem involves computing the final amount in an account after 20 years of annual $10,000 deposits with 4% interest compounded semi-annually. By applying the future value of an annuity formula and inputting the correct values, we can determine the total amount at the end of the specified period.
Step-by-step explanation:
To calculate the final amount in the account after 20 years with an initial deposit of $10,000 each year at an interest rate of 4% compounded semi-annually, we use the future value of an annuity formula:
FV = P × { [ (1 + r/n)^(nt) - 1 ] / (r/n) }
Where:
- P is the payment amount per period ($10,000)
- r is the annual interest rate (0.04)
- n is the number of times interest is compounded per year (2)
- t is the number of years the money is deposited (20)
Inserting the values we get:
FV = $10,000 × { [ (1 + 0.04/2)^(2×20) - 1 ] / (0.04/2) }
After calculating the above expression, we would get the total value of the annuity at the end of 20 years. This kind of problem involves understanding compound interest and annuity calculations, both are important concepts in financial mathematics.
The exact answer would depend on the correct use of the formula and accurate calculations. Typically, a financial calculator or software would be used to compute the exact total amount.