Question

You have decided to save money for your son’s college tuition. You will put away $1,711.00 every six months for the next 12.00 years. If the account will pay 6.00% APR with semi-annual compounding, what is the future value of this investment? (treat as regular annuity)

Answer 1

To calculate the future value of an annuity, we can use the Future Value of an Annuity formula:

\[
FV = PMT \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \(FV\) = Future Value of the annuity
- \(PMT\) = Payment amount per period
- \(r\) = Interest rate per period
- \(n\) = Total number of payments

### Given:
- Payment amount (\(PMT\)) = $1,711.00
- Annual interest rate = 6.00%
- Compounding frequency = semi-annually
- Duration = 12 years

### Steps to solve:
1. **Convert the annual interest rate to a semi-annual rate**:
\[
r = \frac{6\%}{2} = 3\% = 0.03
\]

2. **Calculate the total number of payments (\(n\))**:
\[
n = 12 \, \text{years} \times 2 \, \text{payments per year} = 24 \, \text{payments}
\]

3. **Substitute the values into the formula**:
\[
FV = 1711 \times \frac{(1 + 0.03)^{24} - 1}{0.03}
\]

4. **Calculate \( (1 + 0.03)^{24} \)**:
\[
(1.03)^{24} \approx 2.490
\]

5. **Calculate the future value**:
\[
FV = 1711 \times \frac{2.490 - 1}{0.03}
\]
\[
FV = 1711 \times \frac{1.490}{0.03}
\]
\[
FV \approx 1711 \times 49.67 \approx 85,001.37
\]

### Conclusion:
The future value of the investment after 12 years will be approximately **$85,001.37**.