Which of the following will increase the present value of an annuity, assuming all other factors remain constant?

• A. Decreasing the number of periods
• B. Increasing the discount rate
• C. Decreasing the amount of each payment
• D. Decreasing the discount rate

Answer: (D)

Verified step by step guidance

1. Understand the concept of present value of an annuity: The present value of an annuity is the current worth of a series of future payments, discounted at a specific rate. It is influenced by factors such as the number of periods, the discount rate, and the payment amount.
2. Recall the formula for the present value of an annuity: \( PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \), where \( PV \) is the present value, \( P \) is the payment amount, \( r \) is the discount rate per period, and \( n \) is the number of periods.
3. Analyze the impact of decreasing the discount rate: A lower discount rate \( r \) reduces the denominator in the formula, making the fraction larger. This increases the present value of the annuity because future payments are discounted less heavily.
4. Compare the other options: Decreasing the number of periods \( n \) reduces the total number of payments, which decreases the present value. Increasing the discount rate \( r \) increases the denominator, reducing the present value. Decreasing the payment amount \( P \) directly reduces the present value.
5. Conclude that decreasing the discount rate increases the present value of an annuity, as future payments are discounted less, making their present value higher.