What is the present value of an ordinary annuity of \$400 invested each year for 12 years at an annual interest rate of 6%? (Round your answer to the nearest dollar.)

• A. \$3,534
• B. \$5,200
• C. \$2,900
• D. \$4,800

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of present value of an ordinary annuity. It represents the current worth of a series of equal payments made at regular intervals, discounted at a specific interest rate.
2. Step 2: Use the formula for the present value of an ordinary annuity: \( PV = P \times \frac{1 - (1 + r)^{-n}}{r} \), where \( P \) is the payment amount, \( r \) is the annual interest rate (expressed as a decimal), and \( n \) is the number of periods.
3. Step 3: Substitute the given values into the formula: \( P = 400 \), \( r = 0.06 \), and \( n = 12 \). The formula becomes \( PV = 400 \times \frac{1 - (1 + 0.06)^{-12}}{0.06} \).
4. Step 4: Calculate the term \( (1 + r)^{-n} \), which is \( (1 + 0.06)^{-12} \). This represents the discount factor for 12 periods at a 6% annual interest rate.
5. Step 5: Compute the fraction \( \frac{1 - (1 + r)^{-n}}{r} \) and multiply it by \( P \) (the payment amount) to find the present value of the annuity. Round the result to the nearest dollar.