a) The future value of Regina's annuity is approximately $17,784.67.
b) The total interest earned on her annuity is approximately $9,784.67.
Calculating Future Value and Total Interest
Here's how to find the future value and total interest earned for Regina's annuity:
**1. Define variables:**
* Deposit amount (D) = $2,000
* Interest rate per period (i) = 6% / 2 = 3% (since interest is compounded semiannually)
* Number of periods (n) = 4 years * 2 periods/year = 8 periods
**2. Calculate the future value (FV):**
We can use the formula for the future value of an ordinary annuity:
FV = D * [(1 + i)^n - 1] / i
Substituting the values:
FV = $2,000 * [(1 + 0.03)^8 - 1] / 0.03
FV ≈ $17,784.67
**3. Calculate the total interest earned:**
The total interest earned is the difference between the future value and the total amount deposited:
Total interest = FV - (D * n)
Total interest = $17,784.67 - ($2,000 * 8)
Total interest ≈ $9,784.67
Therefore:
* a) The future value of Regina's annuity is approximately $17,784.67.
* b) The total interest earned on her annuity is approximately $9,784.67.