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.