Final answer:
The accumulated amount in the annuity where $80 is invested semiannually for 10 years at a 6.5% interest rate, compounded semiannually, is approximately $2572.15.
Step-by-step explanation:
To determine the accumulated amount in an annuity where $80 is invested semiannually for 10 years at a 6.5% interest rate compounded semiannually, we need to use the future value formula for an ordinary annuity. The formula is:
FV = P \times \frac{(1 + r)^n - 1}{r}
Where:
- FV is the future value of the annuity.
- P is the payment amount per period.
- r is the interest rate per period.
- n is the total number of payments.
For this problem:
- P = $80 (since $80 is invested every period)
- r = 6.5% / 2 = 3.25% or 0.0325 (because interest is compounded semiannually)
- n = 10 years \times 2 = 20 (since there are two periods per year)
Plugging these values into the formula:
FV = $80 \times \frac{(1 + 0.0325)^{20} - 1}{0.0325}
Calculating the future value:
FV = $80 \times \frac{(1.0325)^{20} - 1}{0.0325} ≈ $80 \times \frac{2.0398873 - 1}{0.0325} ≈ $80 \times 32.151934
FV ≈ $2572.15
Therefore, the accumulated amount in the annuity will be approximately $2572.15.